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A006346
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The Sally sequence: the length of repetition avoided in A006345.
(Formerly M0126)
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2
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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
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OFFSET
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1,4
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COMMENTS
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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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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]
]
];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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