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 A359634 #25 Mar 09 2023 04:21:11 %S A359634 1,1,2,2,3,3,4,3,4,5,4,5,6,4,5,6,7,6,7,8,5,7,8,9,7,6,8,9,10,6,9,10,11, %T A359634 9,8,10,11,12,9,10,9,11,12,13,7,12,13,14,12,11,13,14,15,11,13,11,14, %U A359634 15,16,13,6,14,13,15,16,17,13,15,12,16,17,18,15,8,16,14,17,18,19,15,16,12,17,14,18,19,20 %N A359634 a(0)=1 and thereafter a(n) is the length of the longest contiguous group of terms in the sequence thus far that add up to n; if no such group exists, set a(n)=0. %C A359634 If a zero appears, it is not counted as a term in a contiguous grouping. For example, if (10, 30, 0, 60) is our longest group to sum to 100, this counts as 3 terms, not 4. However, in 50 million terms (computed by _Kevin Ryde_), a zero has not appeared. Why is this? %C A359634 How does the lower envelope of this sequence behave? %H A359634 Rémy Sigrist, <a href="/A359634/b359634.txt">Table of n, a(n) for n = 0..10000</a> %H A359634 Rémy Sigrist, <a href="/A359634/a359634.txt">C program</a> %e A359634 a(6) is 4 because in the sequence thus far (1,1,2,2,3,3), the longest run of consecutive terms that sums to 6 is (1,1,2,2), which is 4 terms. %o A359634 (C) See Links section. %Y A359634 Cf. A331614, A358537. a(1-16) in A138099 are the same. %K A359634 nonn %O A359634 0,3 %A A359634 _Neal Gersh Tolunsky_, Jan 08 2023