A094840 - OEIS

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

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OFFSET

1,5

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

Table of n, a(n) for n=1..100.

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

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 *)

CROSSREFS

Cf. A090822, A006345, A093921, A093914.

Cf. A006345.

Sequence in context: A049236 A356229 A244259 * A035218 A237442 A277070

Adjacent sequences: A094837 A094838 A094839 * A094841 A094842 A094843

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 26 2004

STATUS

approved