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 A006346 The Sally sequence: the length of repetition avoided in A006345. (Formerly M0126) 2
 0, 1, 1, 2, 1, 3, 1, 1, 3, 2, 1, 6, 3, 2, 1, 3, 1, 1, 6, 3, 2, 4, 1, 1, 3, 2, 1, 3, 1, 6, 4, 2, 1, 2, 4, 3, 1, 8, 3, 2, 1, 6, 3, 2, 1, 3, 1, 1, 6, 3, 2, 4, 1, 1, 3, 2, 1, 3, 1, 30, 6, 3, 2, 4, 1, 1, 3, 2, 1, 3, 1, 6, 4, 2, 1, 2, 4, 3, 1, 8, 3, 2, 1, 6, 3, 2, 1, 3, 1, 1, 6, 3, 2, 4, 1, 1, 3, 2, 1, 3, 1, 6, 4, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS In the first 1000 terms, only patterns of lengths 0, 1, 2, 3, 4, 6, 8, 24, 30 and 108 are avoided. - T. D. Noe, Oct 14 2006 In the first 20000 terms, patterns of lengths 0, 1, 2, 3, 4, 5, 6, 7, 8, 16, 18, 24, 30, 108, 528, 552, 1298, 2752, 5876 are avoided. - Robert Israel, Jun 22 2015 In the first 10^6 terms, patterns of lengths 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 24, 30, 36, 60, 72, 108, 318, 372, 414, 420, 444, 522, 528, 546, 552, 1280, 1292, 1298, 1632, 2620, 2752, 5876, 6203, 6218, 13912, 14312, 17220, 17580, 31532, 87650 are avoided. - Ray Chandler, Jun 24 2015 REFERENCES N. S. Hellerstein, personal communication to N. J. A. Sloane. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Robert Israel and Hugo van der Sanden, Table of n, a(n) for n = 1..50000 (1..1000 from T. D. Noe, 1001..20000 from Robert Israel) N. Hellerstein, Letter to N. J. A. Sloane, 1978 N. Hellerstein, M. Gardner, & S. Kim, Correspondence related to the Linus and Sally sequences, 1977 N. J. A. Sloane, Illustration of initial terms Eric Weisstein's World of Mathematics, Sally Sequence. MAPLE LDS:= proc(L)   local Cands, r, m;   Cands:= {\$1..floor(nops(L)/2)};   r:= 0;   for m from 1 while nops(Cands) > 0 do      Cands:= select(c -> L[-m] = L[-c-m], Cands);      if min(Cands) = m then         r:= m;         Cands:= subs(m=NULL, Cands);      fi    od;    r end proc: A:= 1: B:= 0; for n from 2 to 1000 do   a1:= LDS([A, 1]);   a2:= LDS([A, 2]);   if a1 < a2 then A:= A, 1; B:= B, a2 else A:= A, 2; B:= B, a1 fi; od: seq(B[i], i=1..1000); # Robert Israel, Jun 22 2015 MATHEMATICA max = 120; 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}; B = {0}; For[n = 2, n <= max, n++,   a1 = LDS[Append[A, 1]];   a2 = LDS[Append[A, 2]];   If[a1 < a2,     AppendTo[A, 1]; AppendTo[B, a2],     AppendTo[A, 2]; AppendTo[B, a1]   ] ]; Table[B[[i]], {i, 1, max}] (* Jean-François Alcover, Jun 08 2018, after Robert Israel's Maple program *) CROSSREFS Cf. A006345. Sequence in context: A212623 A229214 A218578 * A244740 A088742 A256435 Adjacent sequences:  A006343 A006344 A006345 * A006347 A006348 A006349 KEYWORD nonn,nice,easy,look AUTHOR EXTENSIONS More terms from Naohiro Nomoto, May 21 2001 STATUS approved

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Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)