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A001955
Beatty sequence of 1 + 1/sqrt(11).
(Formerly M0615 N0225)
2
1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 74, 75, 76, 78, 79, 80, 81, 83, 84, 85, 87, 88
OFFSET
1,2
COMMENTS
From R. J. Mathar, Feb 12 2011: (Start)
The value of 1+1/sqrt(11) = 1.30151134457.. is close to (sqrt(13)-1)/2 = 1.3027756377..., so the early terms of the sequence are similar to A184480.
According to the Fraenkel article, the complementary sequence is defined by floor(n*(1+sqrt(11))). (End)
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
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.
MAPLE
A001955 := proc(n) local x ; x := 1+1/sqrt(11) ; floor(n*x) ; end proc:
# for the complementary sequence
A001955compl := proc(n) local x ; x := 1+sqrt(11) ; floor(n*x) ; end proc:
seq(A001955(n), n=1..100) ; # R. J. Mathar, Feb 12 2011
MATHEMATICA
Table[Floor[n*(1 + 1/Sqrt[11])], {n, 1, 65}]
CROSSREFS
Sequence in context: A045671 A276341 A098572 * A184480 A194375 A188222
KEYWORD
nonn
EXTENSIONS
More terms from Robert G. Wilson v, Nov 02 2000
STATUS
approved