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%I #13 Aug 08 2015 20:14:59
%S 1,1,1,1,2,1,2,1,1,2,2,1,2,2,2,1,2,1,1,2,3,1,2,1,1,2,2,1,2,1,2,3,1,1,
%T 2,2,2,1,1,2,2,1,2,2,2,1,2,1,1,2,3,1,2,1,1,2,2,1,2,1,2,2,3,1,2,1,1,2,
%U 2,1,2,1,2,3,1,1,2,2,2,1,1,2,2,1,2,2,2,1,2,1,1,2,3,1,2,1,1,2,2,1
%N a(1) = 1; for n > 1, a(n) = curling number of (b(1),...,b(n-1)), where b() = Linus sequence A006345.
%C The curling number of a finite string S = (s(1),...,s(n)) is the largest integer k such that S can be written as xy^k for strings x and y (where y has positive length).
%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 <a href="/index/Cu#curling_numbers">Index entries for sequences related to curling numbers</a>
%p fd := fopen("b006345.txt",READ) : a006345 := [] : bf := fscanf(fd,"%d %d") : while nops(bf) <> 0 do a006345 := [op(a006345), op(2,bf) ] ; bf := fscanf(fd,"%d %d") ; od: curlN := proc(L) local a,k,klen,Llen,y ; a := 1 ; Llen := nops(L) ; for klen from 1 to floor(Llen/2) do y := op(Llen-klen+1..Llen,L) ; for k from 2 to floor(Llen/klen) do if op(Llen-k*klen+1..Llen-(k-1)*klen,L) = y then if k > a then a := k ; fi ; else break ; fi ; od: od: RETURN(a) ; end: A094840 := proc(n) global a006345 ; if n = 1 then 1; else curlN( [op(1..n-1,a006345)] ) ; fi ; end: for n from 1 to 100 do printf("%d, ",A094840(n)) ; od: # _R. J. Mathar_, Dec 07 2007
%Y Cf. A090822, A006345, A093921, A093914.
%Y Cf. A006345.
%K nonn
%O 1,5
%A _N. J. A. Sloane_, May 26 2004
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