This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384729 #12 Jun 16 2025 01:06:30 %S A384729 1,2,4,8,13,21,31,45,66,81,97,123,148,182,204,252,291,324,352,415,486, %T A384729 540,651,706,792,838,928,1046,1134,1228,1358,1407,1512,1624,1869,1938, %U A384729 2087,2170,2367,2480,2608,2765,3033,3080,3232,3567,3605,3797,3950,4267,4505,4677,5064,5290,5480,5655,6059,6507,6892,6967 %N A384729 A B_2-sequence with reciprocal sum > 2.1615. %C A384729 This is the B_2 sequence with largest reciprocal sum that is known to the author, as of the date of submission. The reciprocal sum of the first 1010 terms, which are given in the attached b-file, is 2.16150003... This already provably exceeds the reciprocal sum of the infinite sequence by R. Lewis (A046185), defined by greedy extension of a sequence of 68 terms (e.g., compute R. Lewis' sequence to 1600 terms, then bound the remainder using the result of B. Lindström on the maximum cardinality of B2-sequences with elements in [1, N]). By extending this sequence greedily after the first 1010 terms, a larger reciprocal sum can obviously be achieved. %C A384729 This sequence first differs from A046185 at the 25th term. %C A384729 This sequence was found by the author by using a combination of beam search and batch greedy algorithm, as part of an experiment to evaluate LLM code generation and mathematical reasoning (all code was written by the LLM, though with significant prompting). %H A384729 Logan J. Kleinwaks, <a href="/A384729/b384729.txt">Table of n, a(n) for n = 1..1010</a> %H A384729 Rachel Lewis, <a href="https://oeis.org/A005282/a005282.pdf">Mian-Chowla and B2 sequences</a>, 1999. %H A384729 Bernt Lindström, <a href="https://doi.org/10.1016/S0021-9800(69)80124-9">An inequality for B_2-sequences</a>, Journal of Combinatorial Theory, Volume 6, Issue 2 (1969), 211-212. %H A384729 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/B2-Sequence.html">B_2-Sequence.</a>. From MathWorld--A Wolfram Web Resource. %Y A384729 Cf. A046185 (R. Lewis), A005282 (Mian-Chowla). %K A384729 nonn %O A384729 1,2 %A A384729 _Logan J. Kleinwaks_, Jun 08 2025