A094840 a(1) = 1; for n > 1, a(n) = curling number of (b(1),...,b(n-1)), where b() = Linus sequence A006345.

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, May 26 2004

Keywords

• nonn

Comments

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).

Links

• 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, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
• 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 [pdf, ps].
• Index entries for sequences related to curling numbers

Crossrefs

Cf. A090822, A006345, A093921, A093914.

Cf. A006345.

Programs

Maple

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

Mathematica

nmax = 100;
LDS[L_] := Module[{Cands, r, m}, Cands = Range[Floor[Length[L]/2]]; r = 0; For[m = 1, Length[Cands] > 0, m++, Cands = Select[Cands, L[[-m]] == L[[-# - m]]&]; If[Min[Cands] == m, r = m; Cands = ReplaceAll[Cands, m -> Nothing]]]; r];
A = {1};
For[n = 2, n <= nmax, n++, If[LDS[Append[A, 1]] < LDS[Append[A, 2]], A = Append[A, 1], A = Append[A, 2]]];
a006345 = A;
curlN[L_] := Module[{a, k, klen, Llen, y}, a = 1; Llen = Length[L]; For[klen = 1, klen <= Floor[Llen/2], klen++, y = L[[Llen - klen + 1 ;; Llen]]; For[k = 2, k <= Floor[Llen/klen], k++, If[L[[Llen - k*klen+1 ;; Llen - (k-1)*klen]] == y, If[k > a, a = k] , Break[]]]]; Return[a]];
A094840[n_] := If [n == 1, 1, curlN[a006345[[1 ;; n-1]]]];
Table[A094840[n], {n, 1, nmax}] (* Jean-François Alcover, Oct 18 2024, after Maple programs *)