A missed opportunity

I rarely go anywhere without my camera and even at home it is always close by. Last night I lent the Nikon to my daughter (for today) and this morning I woke up to winter wonderland: delicate heaps of snow on thin branches — already only a memory just a few hours later. I'll recall my maplepan captured 2 March 2003 (saved photo #52 of my previous Coolpix).

80000 Ruth-Aaron pairs

I've added another 10000 Ruth-Aaron pairs to my list: 80000 factored pairs @ 10.1 MB.

70000 Ruth-Aaron pairs

I've added another 10000 Ruth-Aaron pairs to my list: 70000 factored pairs @ 8.8 MB.

Komets and planits, oh my

Lars Blomberg and I have been busy populating entries in a Google docs spreadsheet that extrapolates "komet" k2 (A038834 <-> A038807) to k6, k11, k13, ... k781: 250 kometary path fragments (and 5 planits) in all. I have had a (much smaller) version of this table as long ago as 1997 but it is certainly nice to see it updated, extended, and out in the open. Almost all of the really large numbers in the chart were calculated by Lars.

60000 Ruth-Aaron pairs

I have added another 10000 Ruth-Aaron pairs to my list: 60000 factored pairs @ 7.6 MB. I was tempted to run the third Mathematica on this effort — cutting my expected completion date by a couple of weeks — but, on Saturday night, I started Mathematica 8 on a different venture: duplicating the extension of A038807 sent me by Lars Blomberg last summer.

Reality check

By this morning, Charles Greathouse and Donovan Johnson had calculated, respectively, the sixth and seventh terms of the sequence that I mentioned in my last entry: A185584. At that point, my own effort had only reached 2 billion. Ordinarily, I might have let things run — or started a new search beginning with the larger value — but I thought better of it.

A number of folk thought it was a good idea to prepend zero to the sequence — which, in my mind, lacked logic — and I objected*. Nevertheless, it was added to the submitted sequence — but later dropped, after I pointed out that the closely related A064510 lacked the zero.

*The crux of my objection was that the primary sense of the word "sum" is an aggregate of two or more things. Aggregating one thing is already a stretch but I'll buy it. Aggregating no things? { } != {0} but (apparently) Apply[Plus, { }] == 0.

An unexpected bonus

Claudio Meller today asked Sequence Fanatics about an extension to the sequence 1, 130, 1860, 148480, 3039520, ... So I fired up Mathematica 8 on my wife's iMac and started a search for the next term. I had indicated here on Saturday my expectation that doing so would degrade the performance of Mathematica 6 and Mathematica 7, concurrently running their respective Ruth-Aaron numbers compilations, but when I consulted the computer's Activity Monitor, I found — to my surprise, and delight — all three Mathematica kernels running at ~100%. The effect — and I wonder if it is just the appearance of a processing-power benefit — may be due to hyper-threading.

Snow big deal

Here in Toronto, they certainly oversold the snowmageddon that was to befall us today. Nevertheless, our school boards — concerned that it had been over 12 years since the last one — decided to declare a snow day. The kids were happy, at least. My photo was taken 50 days ago.