Saturday, June 20, 2020

Lydia, oh Lydia

I was looking through some of my old letters to the editor (mostly to The Globe and Mail) in my online library access to local newspapers when I noticed a 1936 Daily Star hit for my surname "Havermann":
The story had been picked up by a good number of other newspapers. Here is a transcribed version from Whitewright TX (July 9):

Love in his heart, a $13 old-age pension check in his pocket and a 16-year-old bride at his side, Oscar Crawford, 66, Tuesday retired to his eighteen-acre farm for the first honeymoon of his life. Crawford on Sunday received his first State old-age pension check. At noon, he appeared at the Colorado County courthouse with Miss Lydia Havermann, 16, at his side. Clerks declined, however, to issue a marriage license until the father of the bride, William Havermann, appeared and gave his consent. While the father looked on approvingly, County Judge H. P. Hahn read the marriage ceremony. The bride and bridegroom left immediately for the C. W. Ellinger farm, five miles east of Columbus, where the bridegroom is cultivating eighteen acres.

There's a follow-up, datelined UP, Austin TX (July 10). My transcribed version is via the Big Spring Daily Herald:

Oscar Crawford, 66-year-old Colorado county farmer, who recently married Lydia Havermann, 16, may have increased his income by so doing, or he may have lost it entirely. Crawford married Miss Havermann in Columbus on the day that he received his first old age assistance check from the state. The check was for $13. "There is a possibility that his pension check may be increased," Orville S. Carpenter, old age assistance director, said here. "Since he is married he now shares his property with his wife. Thus his income is only half as much." This is the first of such cases to arise since distribution of the checks was begun July 1. Section two of the old age assistance act provides, however, that he can receive assistance only if he "has no wife able to furnish him adequate support." The word adequate is not defined.

The marriage was easy to verify:
Somewhat more difficult was what became of the bride and groom. It had me stymied but my research associate, Marlene Frost, quickly found a large number of relevant documents. First off, we have Oscar's death certificate:
Oscar is shown as having been born on 12 Dec 1869 and dying on 21 Dec 1939. The cause of death appears to be under investigation (the word is "inquest"; thanks Alfy and Cathy for deciphering that). Oscar is "divorced", although (annoyingly) his former partner is referred to only as "widowed". The undertaker is noted as "Wm. Havermann", Lydia's father. William may well have buried Oscar but he was a farm hand, not an undertaker.

Lydia's name appears in the April 1930 census (Fayette County TX) showing her as being 7 years old:
That would have made her only 13 when she married Oscar and 17 when he died. Lydia is not with her family in the April 1940 census. Over the years, the 'r' in this Havermann clan appears to have been dropped. Lydia's parents and three of her four brothers may be found in Sealy Cemetery. Her brother Arnold Havemann (born 24 Jul 1931) is married to a Gloria Lois Abel (born 20 Jul 1937) and they have two children, Charles Arnold Havemann (born 28 Mar 1960) and Tracy Kim Semmler (born 5 Nov 1963).

After considerable digging, Marlene finally unearthed Lydia's birth certificate:
She was named Elzie (born 19 Nov 1922). If one thinks of the name as being a shortened Liz'beth then Lydia shares with that the initial sound. It seems that Elzie may have run away from her marriage to Oscar Crawford and took on an assumed name, ending up in Atoka County, Oklahoma. She had a son, Jimmie Roe Boggs (born 5 Oct 1938). In May 1941, as Katie Belle Boggs, she married a 42-year-old Homer Goodson and bore him eight children. In 1953, her father signed an affidavit changing her name from Elzie to Katie Bell:
Katie Bell died in 1971 and has a final resting place in Farris, Oklahoma. Note that the birth year on her headstone is incorrect.

Tuesday, June 09, 2020

Bill Blair

According to a Canadian Press story today, public safety minister Bill Blair says police misconduct is indefensible. Yet ten years ago, under his leadership, he was defending just such misconduct.

Sunday, June 07, 2020

Late evening family outings

8:03 pm: BBQ/Kumbaya behind 1662 Weston Rd. (distancing? masks? garbage!)

Early morning family outings

5:36 am: baby raccoons climbing our backyard maple tree
5:49 am: nine goslings and proud parents on the Humber river

Thursday, June 04, 2020

Stop!


Squirrels practice physical distancing by running for the nearest tree. This squirrel quickly learned that the square metal post holding up its stop sign wasn't very arboreal.

Yes, we have no plain bagels

We had another grocery order/delivery yesterday. We're good on most of the essentials (bathroom tissue, paper towels, canned goods, bread) but I'm having difficulty acquiring my plain bagels which have been "out of stock" for a while. In yesterday's order I was prepared to go poppy-seed or even sesame-seed, but they weren't available either. The "everything" bagel was a dollar more than what I'm used to paying for a 6-pack and I wasn't sure from the pictured packaging that it was anything more than poppy and sesame seeds on a plain bagel. So I gambled. Alas, they also contained dried onion and roasted garlic, which are anathema to me. I hope the birds aren't as fussy.

Sunday, May 24, 2020

Time flies

In a recent three-and-a-half-hour video homage to John Conway, one of the participants, Siobhan Roberts, recalls Conway telling her that "time flies like an arrow; fruit flies like a banana." Roberts has written a biography of Conway. Of all the stories she might have used to illustrate the man's wit, this one struck me as odd — since of course the quote wasn't a Conway original.

Sometimes attributed to Groucho Marx, quote investigator "Garson O'Toole" (Gregory F. Sullivan) got it right in 2010 when he traced the core of the quotation to Anthony Oettinger, quoting from Oettinger's September 1966 Scientific American article touching on the subject of grammar by computer (time flies vs. fruit flies; the complication is mentioned as early as 1963 in the Harvard Alumni Bulletin). O'Toole: "By 1982 or before someone juxtaposed the sentences to yield a funny combination which was then assigned to Groucho Marx."

The April 1975 issue of Computers and People already had the juxtapositioning. Lawrence M. Clark wrote "Computer Programs that Understand Ordinary Natural Language" (pages 14-19, 23; page 14 reproduced here, quotation boxed in green). It gets better. Clark's three sentences appeared already in the November 1966 issue of Computers and Automation (different title, same publication). Neil Macdonald (a pseudonym for Edmund Berkeley) wrote a short "Research on Meaning in Programming Languages" (page 10, reproduced here). It is "peach" instead of "banana" but that is not as important as the date.

Saturday, May 23, 2020

Where was Weston's Grammar School?

The Toronto Public Library has photo of a "Weston High School" located on the south side of King Street, west of Elm Street, not far from my parents' former house on Joseph Street. I had never known of a school having been at that location and that piqued my curiosity.

Cruickshank and Nason's "History of Weston" has the school "about a quarter-mile from the Main Street" which would put it closer to Rosemount Ave. than to Elm St. To resolve the location, I looked at a 1913 map that showed structures:


The red brick building in the middle of the above is my candidate for the Grammar School. Look at all the empty lots around it. To further convince myself:


Note that there is a slight forward protrusion of the left part of the building which matches the outline in the map. Finally, a 1924 map shows that the building is no longer there. Looking at the location today, one would see this.

Saturday, May 16, 2020

What's an hour?


This morning a couple of ovenbirds crashed into our kitchen deck-door glass. The one on its side righted itself after a couple of minutes and they both just lay there in obvious shock. Here's a closeup of the upright one:


Catherine looked it up and said to just leave them for a few hours. And indeed, three hours later they were gone. This has happened before, twenty or more years ago (I am guessing), and — somewhat remarkably — the two birds that crashed into the door back then were also ovenbirds!

When I downloaded the photos for this article, I noticed that the time-stamp didn't seem right. I soon realized that I had forgotten to set the daylight-saving time option on my camera back on March 8. Which meant that I had 209 recent photos in my Apple Photos app that needed to be adjusted by one hour. Fortunately, Photos makes this easy. Unfortunately, the app hung ~70% through the process:


So I force-quit and relaunched the app to see what had been accomplished. I could see that some of the photos had added the hour but many had not. Worse, Photos had not gone through the 209 photos sequentially by date, but rather, somewhat haphazardly — a few each day. This is no doubt some sort of optimization procedure that utilizes multiple cores for speed gain (the same thing happens when one is importing photos from the camera). What Apple Photos did not realize is that my Mathematica was already utilizing all four cores on my Mac to calculate a ParallelTable. Perhaps this is why the application crashed.

Anyways, I now had to step through each day's photos and try to determine which ones had been adjusted and which had not. I had the camera's sequential photo numbers and the fact that many of the shots had been taken within minutes of each other to help me in this endeavour. However, for days (and parts of a day) where I had only taken one photo, this did not help. It took me another hour or so to step through my backup and check each photo's original time. Only later did I notice that the get-info on even the modified-time photos still showed the original time stamps.

All in all, it took me longer, I think, to correct all that Exif (when did they stop using all-caps?) data than it took those birds to recover. Moreover, I had to add an hour to the "posted" time on my Echo Beach post because I had originally cheated by back-timing that post to match the then-thought-to-be-correct photo time (to give it a more stream-of consciousness feel).

Thursday, May 14, 2020

Unfasten your safety belt


Two months ago we were strapped in for a year-or-two rollercoaster ride. Many bought into the lockdown as a necessary — but decidedly time-limited — mitigation. Two months at home seems to be about as much as the public can bear. It will be an interesting summer.

Sunday, May 10, 2020

Wanted

A virus with no sexual drive
Was wantin' to only survive.
But its number then grew
Exponential to two,
Which is odd since it wasn't alive.



with apologies to Randall Munroe

Thursday, May 07, 2020

Ten random-start worlds in Rule 193

I first wrote about Rule 193 here, back in 2014. I decided to revisit the cellular automaton by setting up ten random-start evolutions:

0                           1                           2                           3                           4
5                           6                           7                           8                           9
Clicking on each panel will get you a larger version of that panel. Clicking on the numbers underneath each panel will get you the individual evolutions. The pictures are large: 14714 by 8508 pixels (~20 MB). Your browser will likely shrink each one to fit the browser window, so be sure to click/expand it to see all the glorious detail.

If you think of the downward-moving "lines" as particles, a lot of "physics" happens as the particles collide. How many different particles can you distinguish?

Saturday, May 02, 2020

Only eight


This typewritten table of the decimal expansions of powers of two up to 2^115 dates to when I was fourteen years old. My fascination then with powers of two almost certainly arose as a consequence of having encountered the wheat and chessboard problem. I would have calculated the numbers by hand and the typing layout suggests a slight obsession with presentation decorum, a handicap I've endured to the present day. The digit after the power is the digital root.

I recently had occasion to extend OEIS sequence A305942, the number of decimal powers of two having exactly n digits zero. For any given n, that number is fairly constant (on average a little over 33) but there is significant variation. For n up to 295000, I have found a zero-count as high as 62 and as low as 11. Checking other digits in the same range, I find a high of 65 and a low of 8 (see below). These extrema are outliers of course and statistics might suggest that we can find larger-than-65 and smaller-than-8 examples, if only we chart n large enough. But bear in mind that my current database of n up to 295000 is based on powers-of-two decimal expansions up to 2^10000000. It is not a fast computation.


This graph (click on it to get a better view) shows the number of occurrences (the blue points) of the digit 7 in decimal powers of two from 9100000 to 9240000. The green line represents the value 275923. Although (due to the size of the points and the thickness of the line) it may seem that there are dozens of points on the line, there are in fact only eight (at powers 9141747, 9143624, 9155434, 9163531, 9168298, 9171371, 9174454, and 9190491).

Saturday, April 25, 2020

Fantastic soup

Basic ingredients. Good for what ails ye.

"As a general rule, those who think they know everything about a subject really know very little about it; those who know most feel their lack of knowledge, and are always anxious to learn more."
— The Abstainers' Advocate (1894)

Around 1960, Harold Pullman Coffin cleverly rephrased this as: "The fellow who thinks he knows it all is especially annoying to those of us who do." There's a quotation website that annoyingly confuses this newspaper columnist with creationist Harold Glen Coffin. All of the quotations are Pullman's but the photo and the bulk of the bio is for Glen!

Saturday, April 18, 2020

Bare necessities (reprise)

After my previous attempt at a grocery delivery service I wasn't particularly anxious to go at it again, but it was either that or actually going to the store. I tried the delivery arm of the local Real Canadian Superstore where we usually (i.e., used to) shop. They listed most of the products I was after except bags of big carrots, so I ordered a bag of baby carrots instead. The total for the order was just over $200 and I gave them my credit card info for payment. There's a $4 delivery fee, a 5% service fee, and a suggested 5% tip for my shopper/deliverer. The order arrived a couple of hours ago, a mere 22 hours after I placed the order!

They reduced the 8 cans of green beans that I ordered to 0 cans, 8 cans of lentils to 4, and 8 big containers of yogurt to 3. That's ok. I had ordered 4 two-litre containers of 1% milk. I was brought 4 one-litre containers but they charged me for the two-litre containers. That's not ok. The plain bagels that I ordered were replaced with sesame seed bagels, which might be ok but I won't know till I try one. The 8 PC white-cheddar mac & cheese boxes that I ordered were replaced with KD regular mac & cheese. I thought that was going to be ok but I just made myself a couple of boxes and it's inedible (although I did eat a bit and now I'm feeling queasy). I'm going to have to throw that out and hide the other 6 boxes.

I asked for a refund on the missing milk. I didn't ask for compensation on the mac & cheese because I reported the problem before I tried it. On the plus side, they did deliver all 24 rolls of toilet paper that I ordered!

Update: I went back to the site and asked for a refund on the mac & cheese. After all, it's a business transaction, so why should I shoulder the burden of their mistake? Incredibly, Instacart Support (who seems to be the go-between here) not only refunded the mac & cheese, but also all 4 of the two-litre milks — it should only have been 2 of them. They call it their "customer happiness refund". In return, they hoped I would check their "Good, I'm satisfied" support followup (as opposed to "Bad, I'm unsatisfied"). How could I refuse.

Thursday, April 09, 2020

Unconscionable

Somebody sure is pissed!

Yesterday:


Today:


Even the playground:


Not only has the caution tape been removed but the "Hey there!" sign is gone. Could it be that our neighbourhood exerciser took offence?

The Bottomless Lake

We are falling down,
Down to the bottom
Of a hole in the ground.
Smoke 'em if you got 'em.
I'm so scared, I can hardly breathe.
I may never see my sweetheart again.

John Prine (1946-2020) [on Aimless Love, 1984]

Wednesday, April 08, 2020

Half-way




It has been six months since I started three of my Mac minis on a Leyland prime search from Leyland #302846980 to Leyland #324766364. That range was divided into 18 parts of mostly 1217740 Leyland numbers each and these parts were distributed across the Mac minis for 18 Mathematica programs to each do a probable prime search. The above three pictures show what I see on those Mac minis, each Mathematica window with its own start date/time, subsequent finds, and at the bottom of each window — determined by manual interruption of each program — how far (the middle of the three numbers) it has come in the search.

The how-far numbers are from 47.8% to 51.5% of their respective search spaces, so clearly I have another six months to go before I am done with this section. I count 35 prime finds of which 34 are new (one is a rediscovery of Norbert Schneider's L(34642,707) that he found in December 2017). Somewhat remarkably, the three Mac minis have run for all this time without interruption. They are hooked up to battery backups and what power failures we have had in the last six months have thankfully all been very brief.

Tuesday, April 07, 2020

Hey there!


"Coronavirus-19 ... can live on metal objects for up to 9 days!"

The name of the virus is "severe acute respiratory syndrome coronavirus 2 " or "SARS-CoV-2" for short (the disease that it causes is COVID-19, which will soon enough become Covid-19 as folk tire of the all caps). Of course viruses are not technically alive, so it is better to say that they are detectable on surfaces for a certain period of time. And in my mind at least, it is not at all clear that detectable equals infective.

Saturday, April 04, 2020

Cottontail


I've been spotting cottontails in the neighbourhood on my morning walks for some weeks now. At least that's what I think they are. In and around Denison Park, along Denison Rd. W., even on Sykes Ave. For decades there's been nary a sign of these critters around here. The coyotes came first. Now rabbits. Makes perfect sense!

Thursday, April 02, 2020

Echo Beach


On Echo Beach, waves make the only sound. On Echo Beach, there's not a soul around.

I am sitting on the back deck in the glorious sunshine, listening to some random tunes in my Join-In-Daily playlist. Could life be any sweeter?

Saturday, March 28, 2020

Thursday, March 26, 2020

Bare necessities

Our last grocery shop was on March 11 at the local Real Canadian Superstore. We only go every three or four weeks so it's important to stock up. Alas, already back then they had no bathroom tissue to sell. So on March 17 I decided to try a grocery delivery service, more specifically Grocery Gateway. There's a minimum $50 order so in addition to $30 worth of "Cashmere" I ordered some canned goods. At checkout, the website wouldn't recognize my credit card information so I opted to pay at the door. I tried subsequently to add my credit card information to the account but there was no way to do that. I'm still waiting for their email response to my query about it. But no matter, when the order arrives I'll tap the credit card so that I won't have to push the buttons.


The scheduled arrival for the order was this morning. I was waiting for it by the front steps. When the order was brought to me I asked about the tap limit. I think he said $50. Damn! My original order was for just over $80. But wait, where's the toilet paper? They didn't include it, which put my total owing under $50. But my tap didn't work for some reason so I had to push the buttons.

Sunday, March 22, 2020

My 500th Leyland prime find


This morning, after a four-and-a-half-day wait, I found my 500th and 501st Leyland primes. The above graph extends what I showed for my 200th find. I have now surpassed Anatoly Selevich's 475 such finds that he computed from January 2003 to July 2011.

Generally, I'm happy with the ongoing search. My 54 dedicated Mac-mini cores have been supplemented in the last few months by 6 cores on my old Mac Pro and 4 on a more recent iMac, which have been working on interval #8 to gain time on the overall computation, the length of which I now realize I did not correctly calculate. More specifically, the three Mac minis that have been working the upper half of interval #14 since early October 2019 were thought to complete their task by July of this year. Instead, they will run for a full year, until October 2020. In effect, that pushes the overall expected spring-2021 completion date to the fall of that year.

Thursday, March 05, 2020

Primes describing digit position

On Monday, Éric Angelini posted this to the Sequence Fanatics Discussion list: S = 11, 41, 61, 83, 113, 101, ... with digits 1, 1, 4, 1, 6, 1, 8, 3, 1, 1, 3, 1, 0, 1, ... at positions 1, 2, 3, 4, ...

11 says: "In position 1 is a 1."
41 says: "In position 4 is a 1."
61 says: "In position 6 is a 1."
83 says: "In position 8 is a 3."
113 says: "In position 11 is a 3."
101 says: "In position 10 is a 1."
etc.

Of course, each added prime must be the smallest possible that has not already been used. There's a few early surprises hinting at things to come: 11, 41, 61, 83, 113, 101, 151, 181, 233, 223, 263, 293, 353, 383, 419, 401, 479, 467, 541, 1009, 599, 631, 661, 691, 727, 751, 787, 797, 809, 877, 907, 919, 967, 991, 9001, 1031, ... Term #20 is 1009 because to the end of term #19 we have 53 digits/positions and term #19 says that the next digit (position 54) is a 1. So we need a prime starting with 1 and 1009 is the smallest one that keeps the growing sequence truthful. Term #20 also dictates that in position 100 is a 9. So when we get to term #34 = 991, we now have 99 digits/positions and so the next prime must start with a 9. Why not 997? Because that says that in position 99 is a 7 and we already know that in position 99 is a 1. So we must travel all the way up to 9001 to keep things honest. And that may have repercussions when we get to position 900.

I eventually wrote a Mathematica program that seemed to work extending the sequence. But it was taking a long time finding term #1447. So I had a look at how far it had gotten. Term #1446 was 190901 taking up positions 7006-7011. Perusing the list of prior terms, I saw that positions 7012-7020 and 7022-7024 were already assigned with digits: 191737191?371... Stepping through, 19 is prime, as is 191, but these lie: position 1 is not 9; position 19 is not 1. Continuing, no more primes up to 191737191. Then we can try 1917371911, 1917371913, 1917371917, 1917371919, replacing the ? with 1, 3, 7, 9, but these are not prime either. So we attach the next digit, 3, and replace the ? with 0, 1, 2, 3, ..., 9. We need not go further than 5 because 19173719153, finally, is prime!

So I managed to figure out term #1447 before my program did! In fact, it would not have found it because I had my initial search go up to only 104395301. Here's a graph (click on it) of 1500 terms:


Updates:

Sunday, March 8: I have run into a second large term at #3868. Term #3867 was 301471 taking up positions 21005-21010. Positions 21011-21020 and 21022-21028 were already assigned with digits: 3713793719?9317373... So #3868 is 371379371929 and #3869 is 31737313.

Monday, March 9: This is now OEIS A333085. It needs a decent Mathematica program!

Wednesday, March 11: I have rewritten my original program to run significantly faster. In fact, the new version has already overtaken the number of terms calculated by the old one. Here's an updated graph.

Monday, March 16: I've reached 12000 terms and primes strictly greater than 700000.

Thursday, March 19: Maximilian Hasler has written PARI/GP code for this sequence which he says computes 10000 terms in a few seconds. Unfortunately, I haven't been able to get it to run.

Tuesday, March 31: I've decided to call it quits at 18000 terms. There was another spike at #16966.

Friday, February 28, 2020

Transcription

Yesterday, Futility Closet showcased a nice arithmetical/linguistic limerick that I hadn't previously seen, sourcing it to "Punch, Sept. 29, 1937, via William R. Ransom, One Hundred Mathematical Curiosities, 1953". The Ransom work appears to be typewritten, as evidenced by a Google snippet view from the 1955 book (I think Futility Closet, via Google perhaps, misstated the year):


Already we see some differences from the limerick in the Futility Closet version. Two lines are indented; there are spaces on either side of the equals sign; most importantly, 3/8 actually is 3 over 8. Interest thus whetted, of course we'd like to see the original from Punch:


Oh my! It's written as a sentence, so no capitalizations at the start of the introduced lines; Ransom's 'Maths Master' also is not capitalized; the period after π is a comma; there's a comma after the fraction (to introduce a pause, not necessary in the lines version); the equals sign has no spaces on its sides, but it is extra long (though not as long as Robert Recorde's 1557 original); and the finale: there is no 'why'.

Tuesday, February 18, 2020

The hidden palindromes


I submitted today, on behalf of Éric Angelini, OEIS A332661. The sequence (1, 2, 3, 11, 4, 22, 101, 5, 111, 6, 1001, 7, 88, 77, 8, 1111, 9, 10001, 33, 121, 131, 202, ...) is composed entirely of palindromic (base ten) integers with an added proviso that the products of adjacent terms are also palindromes. We don't see those products there, so I thought I'd show them here:

1. 1 * 2 = 2
2. 2 * 3 = 6
3. 3 * 11 = 33
4. 11 * 4 = 44
5. 4 * 22 = 88
6. 22 * 101 = 2222
7. 101 * 5 = 505
8. 5 * 111 = 555
9. 111 * 6 = 666
10. 6 * 1001 = 6006
11. 1001 * 7 = 7007
12. 7 * 88 = 616
13. 88 * 77 = 6776
14. 77 * 8 = 616
15. 8 * 1111 = 8888
16. 1111 * 9 = 9999
17. 9 * 10001 = 90009
18. 10001 * 33 = 330033
19. 33 * 121 = 3993
20. 121 * 131 = 15851
21. 131 * 202 = 26462
22. 202 * 44 = 8888
23. 44 * 2002 = 88088
24. 2002 * 141 = 282282
25. 141 * 212 = 29892
26. 212 * 1221 = 258852
27. 1221 * 303 = 369963
28. 303 * 2112 = 639936
29. 2112 * 222 = 468864
30. 222 * 3003 = 666666
31. 3003 * 232 = 696696
32. 232 * 10101 = 2343432
33. 10101 * 55 = 555555
34. 55 * 99 = 5445
35. 99 * 555 = 54945
36. 555 * 979 = 543345
37. 979 * 5555 = 5438345
38. 5555 * 9779 = 54322345
39. 9779 * 55555 = 543272345
40. 55555 * 97779 = 5432112345
41. 97779 * 100001 = 9777997779
42. 100001 * 66 = 6600066
43. 66 * 1000001 = 66000066
44. 1000001 * 151 = 151000151
45. 151 * 11011 = 1662661
46. 11011 * 161 = 1772771
47. 161 * 11111 = 1788871
48. 11111 * 171 = 1899981
49. 171 * 101101 = 17288271
50. 101101 * 181 = 18299281
51. 181 * 110011 = 19911991
52. 110011 * 242 = 26622662
53. 242 * 10201 = 2468642
54. 10201 * 313 = 3192913
55. 313 * 20002 = 6260626
56. 20002 * 323 = 6460646
57. 323 * 20102 = 6492946
58. 20102 * 333 = 6693966
59. 333 * 21012 = 6996996
60. 21012 * 404 = 8488848
61. 404 * 111111 = 44888844
62. 111111 * 252 = 27999972
63. 252 * 1001001 = 252252252
64. 1001001 * 191 = 191191191
65. 191 * 1010101 = 192929291
66. 1010101 * 262 = 264646462
67. 262 * 1100011 = 288202882
68. 1100011 * 272 = 299202992
69. 272 * 1101011 = 299474992
70. 1101011 * 343 = 377646773
71. 343 * 200002 = 68600686
72. 200002 * 414 = 82800828
73. 414 * 120021 = 49688694
74. 120021 * 1331 = 159747951
75. 1331 * 12021 = 15999951
76. 12021 * 10301 = 123828321
77. 10301 * 2222 = 22888822
78. 2222 * 20202 = 44888844
79. 20202 * 3113 = 62888826
80. 3113 * 11211 = 34899843
81. 11211 * 4004 = 44888844
82. 4004 * 210012 = 840888048
83. 210012 * 2332 = 489747984
84. 2332 * 30003 = 69966996
85. 30003 * 3223 = 96699669
86. 3223 * 300003 = 966909669
87. 300003 * 3333 = 999909999
88. 3333 * 1002001 = 3339669333
89. 1002001 * 424 = 424848424
90. 424 * 2000002 = 848000848
91. 2000002 * 434 = 868000868
92. 434 * 2001002 = 868434868
93. 2001002 * 444 = 888444888
94. 444 * 2002002 = 888888888
95. 2002002 * 1441 = 2884884882
96. 1441 * 201102 = 289787982
97. 201102 * 10401 = 2091661902
98. 10401 * 21112 = 219585912
99. 21112 * 11311 = 238797832
100. 11311 * 102201 = 1155995511
101. 102201 * 12121 = 1238778321
102. 12121 * 30103 = 364878463
103. 30103 * 12221 = 367888763
104. 12221 * 40004 = 488888884
105. 40004 * 112211 = 4488888844
106. 112211 * 31013 = 3479999743
107. 31013 * 1011101 = 31357275313
108. 1011101 * 4114 = 4159669514
109. 4114 * 1110111 = 4566996654
110. 1110111 * 10501 = 11657275611
111. 10501 * 1111111 = 11667776611
112. 1111111 * 10601 = 11778887711
113. 10601 * 10000001 = 106010010601
114. 10000001 * 282 = 2820000282
115. 282 * 10100101 = 2848228482
116. 10100101 * 292 = 2949229492
117. 292 * 100000001 = 29200000292
118. 100000001 * 353 = 35300000353
119. 353 * 10011001 = 3533883353
120. 10011001 * 363 = 3633993363
121. 363 * 11000011 = 3993003993
122. 11000011 * 454 = 4994004994
123. 454 * 11011011 = 4998998994
124. 11011011 * 2442 = 26888888862
125. 2442 * 20000002 = 48840004884
126. 20000002 * 3443 = 68860006886
127. 3443 * 20011002 = 68897879886
128. 20011002 * 11411 = 228345543822
129. 11411 * 1200021 = 13693439631
130. 1200021 * 12321 = 14785458741
131. 12321 * 1003001 = 12357975321
132. 1003001 * 20302 = 20362926302
133. 20302 * 121121 = 2458998542
134. 121121 * 301103 = 36469896463
135. 301103 * 21212 = 6386996836
136. 21212 * 310013 = 6575995756
137. 310013 * 1012101 = 313764467313
138. 1012101 * 13031 = 13188688131
139. 13031 * 2010102 = 26193639162
140. 2010102 * 12421 = 24967476942
141. 12421 * 2011102 = 24979897942
142. 2011102 * 22022 = 44288488244
143. 22022 * 400004 = 8808888088
144. 400004 * 22122 = 8848888488
145. 22122 * 1020201 = 22568886522
146. 1020201 * 32023 = 32669896623
147. 32023 * 1102011 = 35289698253
148. 1102011 * 22222 = 24488888442
149. 22222 * 2100012 = 46666466664
150. 2100012 * 13131 = 27575257572
151. 13131 * 2101012 = 27588388572
152. 2101012 * 13231 = 27798489772
153. 13231 * 3000003 = 39693039693
154. 3000003 * 13331 = 39993039993
155. 13331 * 10200201 = 135978879531
156. 10200201 * 13431 = 136998899631
157. 13431 * 20100102 = 269964469962
158. 20100102 * 21312 = 428373373824
159. 21312 * 2003002 = 42687978624
160. 2003002 * 30203 = 60496669406
161. 30203 * 1013101 = 30598689503
162. 1013101 * 30303 = 30699999603
163. 30303 * 3001003 = 90939393909
164. 3001003 * 22322 = 66988388966
165. 22322 * 10111101 = 225699996522
166. 10111101 * 10701 = 108198891801
167. 10701 * 11100111 = 118782287811
168. 11100111 * 4224 = 46886868864
169. 4224 * 100010001 = 422442244224
170. 100010001 * 373 = 37303730373
171. 373 * 100101001 = 37337673373
172. 100101001 * 383 = 38338683383
173. 383 * 101000101 = 38683038683
174. 101000101 * 393 = 39693039693
175. 393 * 101010101 = 39696969693
176. 101010101 * 464 = 46868686864
177. 464 * 1000000001 = 464000000464
178. 1000000001 * 474 = 474000000474
179. 474 * 1001001001 = 474474474474
180. 1001001001 * 484 = 484484484484
181. 484 * 1010000101 = 488840048884
182. 1010000101 * 494 = 498940049894
183. 494 * 10000000001 = 4940000000494
184. 10000000001 * 505 = 5050000000505
185. 505 * 110000011 = 55550005555
186. 110000011 * 515 = 56650005665
187. 515 * 110010011 = 56655155665
188. 110010011 * 525 = 57755255775
189. 525 * 1000110001 = 525057750525
190. 1000110001 * 535 = 535058850535
191. 535 * 1100000011 = 588500005885
192. 1100000011 * 545 = 599500005995
193. 545 * 923757329 = 503447744305
194. 923757329 * 5450000545 = 5034477946497744305
195. 5450000545 * 100000000001 = 545000054505450000545
196. 100000000001 * 565 = 56500000000565
197. 565 * 95359 = 53877835
198. 95359 * 565000565 = 53877888877835
199. 565000565 * 938839 = 530444565444035
200. 938839 * 565565 = 530974479035
201. 565565 * 1000000000001 = 565565000000565565
202. 1000000000001 * 575 = 575000000000575
203. 575 * 9119 = 5243425
204. 9119 * 575575 = 5248668425
205. 575575 * 911080119 = 524394939493425
206. 911080119 * 10000100001 = 9110892298922980119
207. 10000100001 * 585 = 5850058500585
208. 585 * 10010001001 = 5855850585585
209. 10010001001 * 595 = 5955950595595
210. 595 * 92829 = 55233255
211. 92829 * 54145 = 5026226205
212. 54145 * 9282992829 = 502627646726205
213. 9282992829 * 546808645 = 5076020730370206705
214. 546808645 * 10000000000001 = 5468086450000546808645
215. 10000000000001 * 606 = 6060000000000606
216. 606 * 1100110011 = 666666666666
217. 1100110011 * 616 = 677667766776
218. 616 * 11000000011 = 6776000006776
219. 11000000011 * 626 = 6886000006886
220. 626 * 11000100011 = 6886062606886
221. 11000100011 * 636 = 6996063606996
222. 636 * 100001100001 = 63600699600636
223. 100001100001 * 707 = 70700777700707
224. 707 * 858 = 606606
225. 858 * 777 = 666666
226. 777 * 858000858 = 666666666666
227. 858000858 * 70007 = 60066066066006
228. 70007 * 88088 = 6166776616
229. 88088 * 7000007 = 616616616616
230. 7000007 * 8580858 = 60066066066006
231. 8580858 * 700007 = 6006660666006
232. 700007 * 880088 = 616067760616
233. 880088 * 7007 = 6166776616
234. 7007 * 88000088 = 616616616616
235. 88000088 * 70000007 = 6160006776000616
236. 70000007 * 85800858 = 6006060660606006
237. 85800858 * 7000000007 = 600606006600606006
238. 7000000007 * 8800088 = 61600616061600616
239. 8800088 * 700000007 = 6160061661600616
240. 700000007 * 11111111 = 7777777777777777
241. 11111111 * 11511 = 127899998721
242. 11511 * 100111001 = 1152377732511
243. 100111001 * 10801 = 1081298921801
244. 10801 * 101101101 = 1091992991901
245. 101101101 * 11611 = 1173884883711
246. 11611 * 110101011 = 1278382838721
247. 110101011 * 11711 = 1289392939821
248. 11711 * 111000111 = 1299922299921
249. 111000111 * 5005 = 555555555555
250. 5005 * 1110000111 = 5555550555555
251. 1110000111 * 5115 = 5677650567765
252. 5115 * 10001010001 = 51155166155115
253. 10001010001 * 1551 = 15511566511551
254. 1551 * 10010101001 = 15525666652551
255. 10010101001 * 1661 = 16626777762661
256. 1661 * 10100000101 = 16776100167761
257. 10100000101 * 1771 = 17887100178871
258. 1771 * 10100100101 = 17887277278871
259. 10100100101 * 1881 = 18998288289981
260. 1881 * 10101010101 = 18999999999981
261. 10101010101 * 2552 = 25777777777752
262. 2552 * 100010010001 = 255225545522552
263. 100010010001 * 646 = 64606466460646
264. 646 * 100100001001 = 64664600646646
265. 100100001001 * 656 = 65665600656656
266. 656 * 1000001000001 = 656000656000656
267. 1000001000001 * 666 = 666000666000666
268. 666 * 1000100010001 = 666066606660666
269. 1000100010001 * 676 = 676067606760676
270. 676 * 1001000001001 = 676676000676676
271. 1001000001001 * 686 = 686686000686686
272. 686 * 1001001001001 = 686686686686686
273. 1001001001001 * 696 = 696696696696696
274. 696 * 10000100100001 = 6960069669600696
275. 10000100100001 * 717 = 7170071771700717
276. 717 * 874478 = 627000726
277. 874478 * 7887 = 6897007986
278. 7887 * 87470107478 = 689876737678986
279. 87470107478 * 100000000000001 = 8747010747800087470107478
280. 100000000000001 * 727 = 72700000000000727
281. 727 * 100110011001 = 72779977997727
282. 100110011001 * 808 = 80888888888808
283. 808 * 110000000011 = 88880000008888
284. 110000000011 * 818 = 89980000008998
285. 818 * 7580990857 = 6201250521026
286. 7580990857 * 8998 = 68213755731286
287. 8998 * 7587447857 = 68271855817286
288. 7587447857 * 1000000000000001 = 7587447857000007587447857
289. 1000000000000001 * 737 = 737000000000000737
290. 737 * 888 = 654456
291. 888 * 737000737 = 654456654456
292. 737000737 * 888000000000888 = 654456654456654456654456
293. 888000000000888 * 1000001001000001 = 888000888888888888888888000888
294. 1000001001000001 * 747 = 747000747747000747
295. 747 * 8274728 = 6181221816
296. 8274728 * 7470747 = 61818399381816
297. 7470747 * 82747255274728 = 618183809101908381816
298. 82747255274728 * 74700747 = 6181281781221871821816
299. 74700747 * 10000000000000001 = 747007470000000074700747
300. 10000000000000001 * 757 = 7570000000000000757
301. 757 * 8421248 = 6374884736
302. 8421248 * 75700000757 = 637488479974884736

Note that there are a few duplicate products. I count 292 distinct entries, nine of which have duplicates: eight with one duplicate and one with two duplicates.

616: 2
8888: 2
666666: 2
44888844: 3
6166776616: 2
39693039693: 2
616616616616: 2
666666666666: 2
60066066066006: 2