%I #16 Feb 08 2023 07:56:57
%S 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 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 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 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 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 Rémy Sigrist, <a href="/A092331/b092331.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 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 Rémy Sigrist, <a href="/A092331/a092331.txt">C program</a>
%H <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a>
%e From _Rémy Sigrist_, Feb 08 2023: (Start)
%e The first terms, alongside an appropriate partition of prior terms, are:
%e n a(n) Prior terms
%e -- ---- -----------------
%e 1 1 N/A
%e 2 1 1
%e 3 2 1|1
%e 4 2 1 1|2
%e 5 3 1 1|2|2
%e 6 1 1 1 2 2 3
%e 7 2 1 1|2 2|3 1
%e 8 2 1 1 2 2|3 1 2
%e 9 3 1 1|2 2|3 1|2 2
%e 10 2 1|1 2 2 3|1 2 2 3
%e (End)
%o (C) See Links section.
%Y Cf. A090822, A091975, A091976.
%K nonn
%O 1,3
%A J. Taylor (integersfan(AT)yahoo.com), Mar 17 2004