[seqfan] Re: Nice nontrivial integer sequence

[Christian Sievers]

On Wed, Mar 01, 2023 at 08:02:29PM -0400, M. F. Hasler wrote:

> Or find a more efficient way to compute just a few more terms? (I put
> "hard,more" in the draft because 15 terms already take 30sec/1min and the
> time seems to increase by a factor 4-5 for each new term. But I'd be glad
> if there's a much better algorithm and it isn't hard after all.)

After 100_000_000 terms and ~2 seconds computing time, i found 59 stable
terms and 2 still moving. I'll put my C program in the attachment.
(Does that make sense? It's less lines than the results...)

Here are my results:

stable no. 2 is 4 after 5 terms
2 is at 5
stable no. 3 is 11 after 15 terms
2 is at 10
stable no. 4 is 29 after 40 terms
2 is at 17
stable no. 5 is 47 after 76 terms
stable no. 6 is 18 after 76 terms
2 is at 25
stable no. 7 is 61 after 79 terms
2 is at 25
stable no. 8 is 165 after 226 terms
2 is at 39
stable no. 9 is 434 after 599 terms
2 is at 57
stable no. 10 is 703 after 1137 terms
2 is at 74
stable no. 11 is 1675 after 2378 terms
2 is at 96
stable no. 12 is 972 after 2647 terms
2 is at 102
stable no. 13 is 2213 after 3185 terms
2 is at 106
stable no. 14 is 10093 after 12306 terms
2 is at 176
stable no. 15 is 17973 after 28066 terms
2 is at 234
stable no. 16 is 25853 after 43826 terms
2 is at 268
stable no. 17 is 59586 after 85439 terms
2 is at 331
stable no. 18 is 33733 after 93319 terms
stable no. 19 is 7880 after 93319 terms
stable no. 20 is 21427 after 93319 terms
stable no. 21 is 56401 after 93319 terms
2 is at 341
stable no. 22 is 204177 after 260578 terms
2 is at 475
stable no. 23 is 147776 after 351953 terms
stable no. 24 is 91375 after 351953 terms
stable no. 25 is 217724 after 351953 terms
stable no. 26 is 126349 after 351953 terms
2 is at 513
stable no. 27 is 414021 after 540370 terms
2 is at 574
stable no. 28 is 287672 after 701693 terms
stable no. 29 is 161323 after 701693 terms
stable no. 30 is 34974 after 701693 terms
stable no. 31 is 48521 after 701693 terms
stable no. 32 is 13547 after 701693 terms
stable no. 33 is 5667 after 701693 terms
stable no. 34 is 9121 after 701693 terms
stable no. 35 is 12575 after 701693 terms
stable no. 36 is 28604 after 701693 terms
stable no. 37 is 16029 after 701693 terms
stable no. 38 is 3454 after 701693 terms
stable no. 39 is 1241 after 701693 terms
stable no. 40 is 269 after 701693 terms
stable no. 41 is 1180 after 701693 terms
stable no. 42 is 3271 after 701693 terms
stable no. 43 is 2091 after 701693 terms
stable no. 44 is 911 after 701693 terms
stable no. 45 is 2464 after 701693 terms
stable no. 46 is 11409 after 701693 terms
stable no. 47 is 20354 after 701693 terms
stable no. 48 is 90361 after 701693 terms
stable no. 49 is 250729 after 701693 terms
stable no. 50 is 160368 after 701693 terms
2 is at 622
stable no. 51 is 551111 after 711479 terms
2 is at 624
stable no. 52 is 1492965 after 2044076 terms
2 is at 825
stable no. 53 is 941854 after 2434819 terms
stable no. 54 is 390743 after 2434819 terms
stable no. 55 is 1011861 after 2434819 terms
stable no. 56 is 621118 after 2434819 terms
2 is at 873
stable no. 57 is 2714847 after 3335965 terms
2 is at 955
stable no. 58 is 15667964 after 18382811 terms
2 is at 1490
stable no. 59 is 44289045 after 59957009 terms
2 is at 1969
after 100000000 terms:
2 is at 2203


All the best
Christian