A182586 a(n) is the unique nonnegative integer m such that the Grundy function of the position [n,m] for the Wythoff game evaluates to 1.

0, 2, 6, 8, 7, 3, 5, 4, 14, 16, 19, 21, 20, 9, 25, 10, 29, 31, 11, 13, 12, 33, 37, 40, 15, 41, 45, 47, 17, 50, 18, 49, 22, 55, 58, 60, 23, 63, 61, 24, 26, 69, 71, 70, 27, 76, 28, 77, 32, 30, 82, 84, 87, 89, 34, 92, 90, 35, 97, 36, 39, 99, 38, 103, 105, 108, 110, 109

Offset

1,2

Links

Table of n, a(n) for n=1..68.

Maple

mex:=proc(S) local s:
for s from 0 while member(s, S) do od:
s:
end:
GW:=proc(a, b) local i:
option remember:
mex({seq( GW(a-i, b), i=1..a), seq(GW(a, b-i), i=1..b),
seq(GW(a-i, b-i), i=1..min(a, b))}):
end:
W1:=proc(i) local b:
for b from 0 while GW(i, b)<>1 do od:
b:
end:
#W1seq(N): list L of length N such that [i, L[i]] is the
#unique position with grundy function value 1.
W1seq:=proc(N) local i:
[seq(W1(i), i=1..N)]:
end:

Crossrefs

Sequence in context: A278081 A329592 A154970 * A011224 A272097 A236676

Adjacent sequences: A182583 A182584 A182585 * A182587 A182588 A182589

Keyword

nonn

Author

John Y. Kim, May 06 2012

Status

approved