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
KEYWORD
AUTHOR
EXTENSIONS
More terms from Naohiro Nomoto, May 21 2001
STATUS
approved