

A001956


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


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Inserting a=3 into the Fraenkel formula, a scale factor alpha = (2a+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 sWythoff sequence, where s(n)=3n. See A184117 for the definition of lower and upper sWythoff 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) 181190
A. S. Fraenkel, How to beat your Wythoff games' opponent on three fronts, Amer. Math. Monthly, 89 (1982), 353361 (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



