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A001955
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Beatty sequence of 1+1/sqrt(11).
(Formerly M0615 N0225)
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Contribution 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)
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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).
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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.
Index entries for sequences related to Beatty sequences
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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
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MATHEMATICA
| Table[Floor[n*(1 + 1/Sqrt[11])], {n, 1, 65}]
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CROSSREFS
| Sequence in context: A187570 A045671 A098572 * A184480 A194375 A188222
Adjacent sequences: A001952 A001953 A001954 * A001956 A001957 A001958
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 02 2000
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