A001956 Beatty sequence of (5+sqrt(13))/2. (Formerly M3327 N1338)

4, 8, 12, 17, 21, 25, 30, 34, 38, 43, 47, 51, 55, 60, 64, 68, 73, 77, 81, 86, 90, 94, 98, 103, 107, 111, 116, 120, 124, 129, 133, 137, 141, 146, 150, 154, 159, 163, 167, 172, 176, 180, 185, 189, 193, 197, 202, 206, 210, 215, 219, 223, 228, 232, 236, 240, 245, 249

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)

Index entries for sequences related to Beatty sequences

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

Complement of A184480.

Cf. A184117, A184482.

Sequence in context: A311439 A311440 A311441 * A311442 A311443 A311444

Adjacent sequences: A001953 A001954 A001955 * A001957 A001958 A001959

Keyword

nonn

Author

N. J. A. Sloane

Status

approved