Sunday, October 12

Climb to a prime


I took on my table of A195264 three years ago. I am still chipping away at the currently-317 primary unknowns (out of 10000), extending ECM-factorization attempts from 2000 to 5000 curves. I'm not yet even half-way through the list. Occasionally factordb will have found for me (over time) the large factors for up to 116-digit composites! And in a handful of cases I have evolved an unknown into a prime — which finishes those unknowns from consideration, but there are plenty more.

I've been a little resentful that I hadn't picked the arguably aesthetically-better (one less arithmetic symbol with which to deal), historically better-known home prime sequence (A037274) on which to while away my time. No matter now: John Conway has offered $1000 for a resolution (problem 5) to term #20 of A195264, not term #49 of A037274 — which he could easily have picked instead. I don't believe that (mathematically) it makes any difference: one is as contrived as the other. Conway's point (I think) is that there exist easily-stated but impossible-to-prove conjectures about such sequences. To collect the $1000 for problem 5, you will almost certainly have to luck into a prime in the evolution, because proving that it doesn't evolve into a prime may well be impossible.

While the prize may spur some to further evolve A195265, it may also impede them from sharing any results of that effort. I hope that's not the case.

Friday, October 3

Time has come


My D5300 has a GPS chip in it. I don't own a mobile phone so this is actually my first acquaintance with the capability. Of course I enabled it, even though I suspect that it will be a drain on the camera's battery. As it turns out, only about one in seven of my photos had the location data embedded in it and a cursory look indicated location placement wasn't necessarily all that close. A handful of waypoints had me on the opposite side of the Humber river from where I actually was!

There is an upside. The camera has a set clock from satellite option and I had turned on this feature. The above photo was captured on September 28, exactly 19 days after my first photo taken just after I manually set the camera's clock. The photo's embedded time-stamp was still in sync with real time, indicated here by a website clock. I may never have to correct the camera clock again.

Wednesday, October 1

Shelfie


My new D5300 does some in-camera filter effects. My sense of photography is journalism — not art — so this seems to me extravagant and unnecessary. (If you want to photoshop, use a computer.) Regardless, I tried it out. This "shelfie" is a color sketch effect and its pastel hues are actually quite pleasant. I shared another shelfie on Google+ last year and there is some overlap with this image. The only other effect I have tried so far is HDR painting which was rather disappointing. I had hoped for better HDR and less painting.

Tuesday, September 30

Moving on

Three weeks ago I got a new brain/body for my (camera) lens. I had been using my Nikon D40X with a Nikkor 18-200mm zoom since 25 October 2007, so long enough. The years of use (over 31000 photographs) had baked some dust onto the camera's sensor and these showed up as smudge spots in blue-sky backdrops — very annoying! I suppose this is fixable by a proper in-shop cleaning but the logistics daunted me. So (instead) I purchased a Nikon D5300. It was my intention to take a whole bunch of photos before evaluating the results — but my iMac's two-year-old hard drive died a week into the picture-taking and it took a whole week to replace it. By then, I had decided to upgrade my lens as well. The Nikkor 18-300mm zoom was a near-identical replacement with a small zoom improvement and — more importantly — a lock that prevented the zoom from unfurling under its own weight, something with which I had been struggling all these years.


Monday, September 29

Where the woodbine twineth


My much-photographed island in the Humber, taken on September 20. Usually I'm high up the bank (behind me) looking down but I wanted to see how close I could get to the egret on the rocks (at bottom right). The woodbine in my title refers to the prominent (red) Virginia creeper (Parthenocissus quinquefolia) climbing up a tree.

Wednesday, August 27

What's on first?

A sequence that I'm currently attempting to extend: _, 91, 3854, 178086, 15469622, ... I've purposely left out the surprising first term.

Update: It is now a sequence in the OEIS.

Thursday, August 14

3329 is a prime balanced factorial

It may appear that the following Mathematica execution took just over an hour. In fact, it has taken me many weeks to be able to write it.

PrimeQ[3329!-7607]

True

DateString[]
NextPrime[3329!-7607]
DateString[]

Thu 14 Aug 2014 08:03:36

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Thu 14 Aug 2014 09:12:03

Tuesday, August 5

A beautiful picture

I have suspected for years that the television picture supplied by the evil Canadian Rogers cable empire was sub-optimal at my Toronto house, owing (I thought) to a less-than-perfect infrastructure situation somewhere upstream. It all came to a head three years ago, as this lengthy complaint to an online Rogers employee attempts to explain. A senior technician did subsequently come to the house and declared my television — not their cabling — to be the problem. And alas, that television did indeed suffer from a defect (unbeknownst to me, as the set was borrowed from my daughter) that prevented proper reception on some channels. Rogers charged me $50 for the technician having to come to my house for no good reason, as it were. In light of the defect, I could not press the issue of sub-optimal reception.

Fast-forward to yesterday morning. I had lost my Teksavvy internet signal (which runs on Rogers' cable) and my television picture was somewhat more degraded than usual (so I knew it was an issue with the cable, not the modem). Rogers demands from Teksavvy a full accounting of the situation before they will issue a ticket for a technician to be sent and so I spent a full hour being interviewed by a Teksavvy employee, gathering modem and network details. Subsequently, Catherine found out from our immediate neighbours that they had lost their Rogers television signal altogether.


Early this morning a couple of Rogers subcontractor vehicles appeared and Catherine learned from their drivers that there were additional houses on the street without a Rogers signal. Unable to fix the problem on their own, they issued a Mayday to Rogers. The Rogers truck (pictured) appeared before ten. By noon I had my internet back — although it was off-again/on-again for several hours as they continued (I guess) to troubleshoot the line. Finally, they were done. I had my internet and when I turned on the television — I had a pristine picture the likes of which I had never seen. So yes, I did have a sub-optimal feed all these years!

Tuesday, July 22

Cousins

I thought Kaya and Bodie were step-siblings. Actually, they are cousins. Kaya came for a visit just now. You can see that we've trimmed Bodie's ears and tail.


Tuesday, July 15

Bodie


We have adopted a genetically modified wolf. The horror! It's been six-and-a-half years since we lost Micky, a wheaten terrier. Late June we took in (for a week) our friends' miniature poodle, Kaya, and I guess it rekindled in Catherine some dog-ownership benefits. Six-month-old Bodie (rhymes with Jodie) and Kaya are cousins.