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A003623
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From a 3-way splitting of positive integers: [[n*phi^2]*phi].
(Formerly M2715)
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17
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3, 8, 11, 16, 21, 24, 29, 32, 37, 42, 45, 50, 55, 58, 63, 66, 71, 76, 79, 84, 87, 92, 97, 100, 105, 110, 113, 118, 121, 126, 131, 134, 139, 144, 147, 152, 155, 160, 165, 168, 173, 176, 181, 186, 189, 194, 199, 202, 207, 210, 215, 220, 223, 228, 231, 236, 241, 244, 249
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Union of A001950 & A003622 & A003623 = A000027.
a(n) is odd if and only if n is odd. [Clark Kimberling, Apr 21 2011]
A005614(a(n)-1)=1 and A005614(a(n))=1, n>=1. Because Wythoff AB-numbers (see the formula section) mark the first entry of pairs of 1s in the rabbit sequence A005614(n-1), n>=1. - From Wolfdieter Lang, Jun 28 2011.
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REFERENCES
| Fraenkel, Aviezri S., Complementary iterated floor words and the Flora game. SIAM J. Discrete Math. 24 (2010), no. 2, 570-588. - From N. J. A. Sloane, May 06 2011
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 10.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Index entries for sequences related to Beatty sequences
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FORMULA
| a(n) = [n*phi] + [n*phi^2] = A000201(n) + A001950(n).
a(n)=2*[n*phi]+n.
a(n)=A(B(n)) with A(k):=A000201(k) and B(k):=A001950(k), k>=1 (Wythoff AB-numbers).
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MAPLE
| A003623:=proc(n) return floor(floor(n*(3+sqrt(5))/2)*(1+sqrt(5))/2); end:seq(A003623(n), n=1..59); # Nathaniel Johnston, Apr 21 2011
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MATHEMATICA
| f[n_] := Floor[ GoldenRatio * Floor[ n * GoldenRatio^2]]; Array[f, 47]
(* another *) Table[n+2Floor[n*GoldenRatio], {n, 1, 100}]
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CROSSREFS
| Cf. A003622.
Sequence in context: A047470 A184401 A190251 * A190463 A190435 A188032
Adjacent sequences: A003620 A003621 A003622 * A003624 A003625 A003626
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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