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 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 = (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 Complement of A184480. Cf. A184117, A184482. Sequence in context: A043333 A037352 A028434 * A189527 A106633 A002004 Adjacent sequences:  A001953 A001954 A001955 * A001957 A001958 A001959 KEYWORD nonn AUTHOR STATUS approved

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