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A003151
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Beatty sequence for 1+sqrt(2); a(n) = floor(n*(1+sqrt(2))).
(Formerly M1033)
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16
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2, 4, 7, 9, 12, 14, 16, 19, 21, 24, 26, 28, 31, 33, 36, 38, 41, 43, 45, 48, 50, 53, 55, 57, 60, 62, 65, 67, 70, 72, 74, 77, 79, 82, 84, 86, 89, 91, 94, 96, 98, 101, 103, 106, 108, 111, 113, 115, 118, 120, 123, 125, 127, 130, 132, 135, 137, 140, 142, 144
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(1)=2; for n>1, a(n+1)=a(n)+3 if n is already in the sequence, a(n+1)=a(n)+2 otherwise.
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Shiri Artstein-avidan, Aviezri S. Fraenkel and Vera T. Sos, A two-parameter family of an extension of Beatty sequences, Discrete Math., 308 (2008), 4578-4588.
L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Pellian representatives, Fib. Quart., 10 (1972), 449-488.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence arXiv:math.NT/0305308
Index entries for sequences related to Beatty sequences
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MAPLE
| Digits:=100:t:=evalf(1+sec(Pi/4)):A:=n->(t*n):seq(floor((t*n)), n=1..60); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 27 2009]
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CROSSREFS
| Complement of A003152.
A001951(n) + n.
Cf. A109250.
Sequence in context: A193600 A190429 A175884 * A189939 A189470 A189681
Adjacent sequences: A003148 A003149 A003150 * A003152 A003153 A003154
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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