Monday, December 24

Go stuff yourself!

When Eric Angelini and Jean-Marc Falcoz submitted to the OEIS on December 3 their stuffable numbers sequence (see my Stuffing post last month), they also submitted a self-stuffable numbers sequence to accompany it. The same day, to the latter I added a 41-term "b-file". On December 6, John Mason replaced that with an 84-term file. Although I had by then calculated more than 41 terms, I would never have reached 84 terms (< 10^15) with my clumsy brute-force effort. Looking at Mason's 84 terms, I noticed (and soon proved to myself) that the numbers 103008000000, 1031008000000, 10311008000000, 103111008000000, ... were the beginning of an infinite family of self-stuffable numbers, an unexpected and utterly delightful emergence.

I rewrote my program for generating self-stuffables and managed 95 terms (< 10^17) by December 12, on which day I submitted my observation about the 103008000000 family. One week later — still waiting for that comment to be approved — I decided to advertise it on the Sequence Fanatics Discussion list. Although I had noted that it was an infinite family, John Mason felt it important to point out that he had extended (but not yet submitted) his b-file and had found 1031111008000000 and 10311111008000000. In order to give John a heads-up, I emailed him privately and told him that I was four days away from finishing my 18-digit terms (<10^18), adding at least three dozen terms (which I had by then calculated) to the 95 terms we had both reached. I asked John if he was working on the 18-digit terms as well. He replied that he wasn't. If he had been, I would have offered to wait until he was done so that we might co-author the extended b-file together.

Two days later (December 21), John posted to the Sequence Fanatics Discussion list that he had calculated the 18-digit terms and had submitted his new 134-term b-file. Interestingly, he left my count at 41. Ouch! Mason had the audacity to complain that he was looking for efficiencies in his program as it had taken him all of eight hours to run. Mine was taking eleven days! To add insult to injury, on December 22 the iMac on which my program was running suffered a kernel panic and — one day short — I lost the completion of it.

Update: On 2 January 2019, Lars Blomberg suggested 165 terms (<10^22) but it was noticed by Ray Chandler that at least one term (21021021021021021021) was missing! On 14 January 2019, John Mason uploaded 145 terms (<10^20) that included Blomberg's missing number.

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