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A003623
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Wythoff AB-numbers: floor(floor(n*phi^2)*phi), where phi = (1+sqrt(5))/2.
(Formerly M2715)
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25
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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
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OFFSET
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1,1
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COMMENTS
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Previous name was: "From a 3-way splitting of positive integers: [[n*phi^2]*phi]."
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. - Wolfdieter Lang, Jun 28 2011
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REFERENCES
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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
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Aviezri S. Fraenkel, The Raleigh game, INTEGERS: Electronic Journal of Combinatorial Number Theory 7.2 (2007): A13, 10 pages. See Table 1.
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FORMULA
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a(n) = 2*floor(n*phi) + n = 2*A000201(n) + 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
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MATHEMATICA
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f[n_] := Floor[ GoldenRatio * Floor[ n * GoldenRatio^2]]; Array[f, 47]
(* another *) Table[n+2Floor[n*GoldenRatio], {n, 1, 100}]
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PROG
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(Python)
from sympy import floor
from mpmath import phi
def a(n): return floor(n*phi) + floor(n*phi**2) # Indranil Ghosh, Jun 10 2017
(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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