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Search: id:A003151
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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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+0
12
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Pellian representatives, Fib. Quart., 10 (1972), 449-488.
Shiri Artstein-avidan, Aviezri S. Fraenkel and Vera T. Sos, A two-parameter family of an extension of Beatty sequences, http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/coatp8.pdf, Discrete Math., 308 (2008), 4578-4588.
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LINKS
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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 (math.NT/0305308)
Index entries for sequences related to Beatty sequences
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MAPLE
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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
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Complement of A003152.
A001951(n) + n.
Cf. A109250.
Sequence in context: A054406 A081841 A027904 this_sequence A059542 A022840 A064995
Adjacent sequences: A003148 A003149 A003150 this_sequence A003152 A003153 A003154
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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