OFFSET
1,1
COMMENTS
Inserting a=3 into the Fraenkel formula, a scale factor alpha = (2-a+sqrt(a^2+4))/2 = (sqrt(13)-1)/2 is obtained, which defines the Beatty sequence A184480. The complementary beta parameter, 1/beta+1/alpha=1, is beta = (5+sqrt(13))/2 = 3+alpha, and defines this sequence here, which is the complement in the positive integers. - R. J. Mathar, Feb 12 2011
Upper s-Wythoff sequence, where s(n)=3n. See A184117 for the definition of lower and upper s-Wythoff sequences. - Clark Kimberling, Jan 15 2011
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 = 1..10000
Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190
A. S. Fraenkel, How to beat your Wythoff games' opponent on three fronts, Amer. Math. Monthly, 89 (1982), 353-361 (the case a=3)
FORMULA
a(n) = floor(n*beta) with beta = (5+sqrt(13))/2 = 3+(sqrt(13)-1)/2 = 4.30277563773199...
MAPLE
A001956 := proc(n) local x ; x := (5+sqrt(13))/2 ; floor(n*x) ; end proc:
A184480 := proc(n) local x ; x := (sqrt(13)-1)/2 ; floor(n*x) ; end proc:
seq(A001956(n), n=1..100) ; # R. J. Mathar, Feb 12 2011
MATHEMATICA
Table[Floor[n*(5 + Sqrt[13])/2], {n, 100}] (* T. D. Noe, Aug 17 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved