

A001954


Wythoff game.
(Formerly M3774 N1539)


4



1, 5, 8, 11, 15, 18, 22, 25, 29, 32, 35, 39, 42, 46, 49, 52, 56, 59, 63, 66, 69, 73, 76, 80, 83, 87, 90, 93, 97, 100, 104, 107, 110, 114, 117, 121, 124, 128, 131, 134, 138, 141, 145, 148, 151, 155, 158, 162, 165, 169, 172, 175, 179, 182, 186, 189, 192, 196, 199
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OFFSET

0,2


COMMENTS

Winning positions in the 2Wythoff game, the upile in Connell's nomenclature; vpile numbers in A001953.
Let s(n) = zeta(3)  sum{1/k^3, k = 1..n}. Conjecture: for n >=1, s(a(n)) < 1/n^2 < s(a(n)1), and the difference sequence of A049473 consists solely of 0s and 1, in positions given by the nonhomogeneous Beatty sequences A001954 and A001953, respectively.  Clark Kimberling, Oct 05 2014


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000
Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181190
J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, 2012; J. Int. Seq. 16 (2013) #13.1.8


FORMULA

a(n) = floor[(n+1/2)*(2+sqrt(2))].


MATHEMATICA

Table[Floor[(n + 1/2) (2 + Sqrt[2])], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)


PROG

(PARI) a(n)=floor((n+1/2)*(2+sqrt(2)))


CROSSREFS

Complement of A001953. Bisection of A003152.
Sequence in context: A186238 A314389 A118520 * A006620 A176628 A314390
Adjacent sequences: A001951 A001952 A001953 * A001955 A001956 A001957


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Michael Somos, Apr 26 2000


STATUS

approved



