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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. 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).
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LINKS
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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.
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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:
seq(B[i], i=1..1000); # Robert Israel, Jun 22 2015
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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]
]
];
Table[B[[i]], {i, 1, max}] (* Jean-François Alcover, Jun 08 2018, after Robert Israel's Maple program *)
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CROSSREFS
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Cf. A006345.
Sequence in context: A212623 A229214 A218578 * A244740 A088742 A256435
Adjacent sequences: A006343 A006344 A006345 * A006347 A006348 A006349
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KEYWORD
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nonn,nice,easy,look
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Naohiro Nomoto, May 21 2001
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STATUS
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approved
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