I have today finished examining the Leyland numbers from 1000800 digits to 1000899 digits and have found no PRPs therein. This adds to my previous search of 1000900 digits to 1000999 digits completed 26 Jan 2024 wherein I found three PRPs. At nine to ten months per search, I am not anxious to try another such interval. Yesterday was the ninth (year) anniversary of my very first Leyland-prime find. That's a long time to be obsessed with the task. I'm going to take a breather.

# Glad Hobo Express

## Friday, October 04, 2024

## Thursday, October 03, 2024

### Éric Angelini (1951-2024)

*two*"signes" in order to make the self-referential closing assertion

*true*. Éric's final

*Cinquante signes*article just misses Michael Branicky's (late Sep. 27) emailed response:

## Friday, September 20, 2024

## Friday, September 13, 2024

### Recycling

One of the pastimes of living where we live is to curtain twitch a credible comprehension of human behaviour, such as it is.

## Thursday, September 05, 2024

### Unknown Havermann

I ran into my older sister's genealogy post on an Unknown Havermann yesterday and I was wondering how it ever came to this. Back in 2010 we had a brief email discussion on the matter (I've made some of my reply-text bold for emphasis):

16 Nov 2010

I read with interest your blog on our family tree. I am amazed that you were able to go back that far. Question: Generation V: Heinrich (living with his mother in 1900) +

[*The Generation-V link is a 2022-updated page. The + is a date-of-death marker. In 2010, I did not yet know that date. I have a Neheim1900 excerpt that lists only some family names.*]

I have a Heinrich who was a child of Sette – born: Jan.30/1901; died: Feb.26/1922 which seems to be at odds with your information that he was a child of Heinrich Havermann and Maria Messelke. Perhaps we are talking about another Heinrich?

17 Nov 2010 reply

**My Heinrich came directly from dad's Stammbuch.** I had scanned a copy of it for my computer but I have since lost that file because of a hard drive failure a couple of years ago. You will have to look at the original (assuming it wasn't thrown out). **The residents-living-in-Neheim-in-1900 list basically confirms the existence of that person. He is old enough to be a Fabrikarbeiter and indeed, because his father died in 1876, he would have been at least 24 years old then.**

18 Nov 2010

Thanks for your email clarifying my inquiry. I do have the "Ahnenpass". This seems to be a booklet that belonged to the relatives in Wattenscheid. Is this the same as the "Stammbuch" that you are referring to. I am willing to share the information with you if you want. Let me know.

18 Nov 2010 reply

[*to part 1*] **Yes**, that sounds like it. **It does have Heinrich as a son of Heinrich, does it not?**

[*to part 2*] No. I have all the information I need.

## Sunday, September 01, 2024

### Goodbye Netflix, hello YouTube Premium

Today is the last day of my long-time (since April 2013) Netflix subscription and the first day of my new YouTube Premium subscription for which I'll be paying $5.64 less per month after my one-month-free trial.

## Thursday, August 29, 2024

### The pore structure of Clostridium perfringens epsilon toxin

[article] BioMoleculePlot3D (ribbons) in Wolfram 14.1: click to enlarge |

## Friday, August 09, 2024

### Alphabetizing the integers

Last month I wrote an article called "Integers, in alphabetical order" that illustrated my then-obsession with the topic. In February 1981, Ross Eckler had an article called "Alphabetizing the integers" (in the magazine Word Ways) that loosely anticipated my exploration.

On page 20 of his article, Eckler notes Philip Cohen's approach to the "Bergerson" problem (find the fixed points for integers 1 to n):

**one** **one** **one** four five five five eight eight

**two** three one four four four five five

two **three** one one one four four

two three six seven one nine

two three six seven one

two three **six** seven

two three six

two three

two

The number of fixed-point counts leads us to OEIS sequence A340671, which provides the actual fixed points in one of the links. Eckler gives us the list-sizes which produce matches for the first twenty integers. I have extended this listing to 100000 integers here. Eckler then notes that 3 appears (I am paraphrasing) in A340671 at positions 13 and 31 and asks for additional values. The third occurrence is at position 201 (then 203, 204, 208, ...). He didn't ask for a first 4, 5, 6, ... appearance as these were clearly beyond his realm of realizability at the time. But here they are:

1 1

2 2

3 13

4 202

5 213

6 2202

7 2213

8 14475

9 233164

10 320200

11 449694

12 2450694

13 4367488

14 4580804

15 4580824

The listing is for the first appearance of 1 to 15, giving the position/index at which it occurs. Michael Branicky found #12 on July 7. I determined #13 to #15 yesterday. The fixed points are added here.

## Tuesday, July 30, 2024

### Fun with digital roots

Éric Angelini's most recent blog is here. I was sufficiently intrigued with his challenge to find larger primes than his 20248751248751248751248751248751248751248751248751 that I gave it a go:

z(41) = 20 grows into z(89), Éric's 50-digit prime.

z(91) = 22 grows into z(280), a 191-digit prime.

z(300) = 35 grows into z(1064), a 766-digit prime.

z(3740) = 238 grows into z(**d**+3737), a **d**-digit (>140000) prime.

Up to this point, we have 151 primes in Z. Their positions/indices are: 2, 3, 4, 20, 21, 23, 26, 29, 31, 34, 37, 38, 40, 89, 280, 281, 284, 287, 290, 291, 293, 296, 299, 1064, 1066, 1073, 1078, 1079, 1081, 1084, 1085, 1144, 1147, 1170, 1171, 1184, 1221, 1262, 1263, 1265, 1268, 1271, 1278, 1280, 1287, 1616, 1617, 1619, 1660, 1665, 1698, 1700, 1703, 1706, 1707, 1712, 1719, 1721, 1724, 1729, 1784, 1787, 1789, 1792, 1897, 1899, 1914, 1919, 1920, 1922, 1965, 1972, 1973, 1978, 1983, 1986, 1993, 1998, 2001, 2022, 2043, 2045, 2064, 2075, 2076, 2097, 2100, 2103, 2104, 2106, 2109, 2112, 2115, 2225, 2242, 2243, 2245, 2248, 2293, 2336, 2338, 2363, 2366, 2369, 2371, 2388, 2393, 2396, 2513, 2516, 2517, 2660, 2693, 2696, 2697, 2699, 2704, 2709, 2724, 2727, 2744, 2747, 2748, 2750, 2795, 2800, 2801, 2803, 2810, 3156, 3183, 3188, 3191, 3204, 3206, 3225, 3290, 3293, 3360, 3427, 3462, 3475, 3477, 3484, 3485, 3487, 3506, 3511, 3512, 3515, 3738. So we are looking for prime #152 (the next one). I've put an indexed file of Z (to 3752) here.

One might suppose that in the absence of a definite **d**, we cannot continue Z. Actually, assuming that **d** exists, we can. What we cannot do is assign indices to the continuation, unless one is ok with:

**d**+3738 239 (prime #153)**d**+3739 240**d**+3740 241 (prime #154)**d**+3741 242**d**+3742 2428**d**+3743 24287

...

I've computed 11288 terms of this continuation but, in order to make the file size smaller, I have removed **d**+7693 to **d**+15024 from view. The file is here. The final term at the bottom (index **d**+15025) is prime #190, a 7348-digit prime.

### Festival!

*****: "Maggie's Farm"

*****minus Paul Butterfield, plus Al Kooper & Barry Goldberg