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 A092331 #16 Feb 08 2023 07:56:57 %S A092331 1,1,2,2,3,1,2,2,3,2,3,2,4,3,3,3,4,1,3,2,2,3,3,3,3,4,2,3,3,4,2,5,2,2, %T A092331 4,3,2,5,2,3,3,2,4,2,3,3,2,3,3,3,3,4,2,3,3,4,4,4,3,3,4,4,4,3,3,3,3,4, %U A092331 4,4,4,4,5,3,4,3,2,3,3,2,3,4,4,3,3,5,3,3,3,4,5,3,3,3,4,3,3,5,3,6,3,3,4,6,2 %N A092331 For S a string of numbers, let F(S) = the sum of those numbers. Let a(1)=1. For n>1, a(n) is the largest k such that the string a(1)a(2)...a(n-1) can be written in the form [x][y_1][y_2]...[y_k], where each y_i is positive (but not necessarily all the same) length and F(y_i)=F(y_j) for all i,j<=k. %C A092331 Here multiplication denotes concatenation of strings. This is Gijswijt's sequence, A090822, except that the 'y' blocks count as being equivalent whenever the sum of their digits is equal. %H A092331 Rémy Sigrist, <a href="/A092331/b092331.txt">Table of n, a(n) for n = 1..10000</a> %H A092331 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2. %H A092331 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>]. %H A092331 Rémy Sigrist, <a href="/A092331/a092331.txt">C program</a> %H A092331 <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a> %e A092331 From _Rémy Sigrist_, Feb 08 2023: (Start) %e A092331 The first terms, alongside an appropriate partition of prior terms, are: %e A092331 n a(n) Prior terms %e A092331 -- ---- ----------------- %e A092331 1 1 N/A %e A092331 2 1 1 %e A092331 3 2 1|1 %e A092331 4 2 1 1|2 %e A092331 5 3 1 1|2|2 %e A092331 6 1 1 1 2 2 3 %e A092331 7 2 1 1|2 2|3 1 %e A092331 8 2 1 1 2 2|3 1 2 %e A092331 9 3 1 1|2 2|3 1|2 2 %e A092331 10 2 1|1 2 2 3|1 2 2 3 %e A092331 (End) %o A092331 (C) See Links section. %Y A092331 Cf. A090822, A091975, A091976. %K A092331 nonn %O A092331 1,3 %A A092331 J. Taylor (integersfan(AT)yahoo.com), Mar 17 2004