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A026352
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a(n) = floor(n*tau) + n + 1 where tau is the golden ratio A001622.
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19
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1, 3, 6, 8, 11, 14, 16, 19, 21, 24, 27, 29, 32, 35, 37, 40, 42, 45, 48, 50, 53, 55, 58, 61, 63, 66, 69, 71, 74, 76, 79, 82, 84, 87, 90, 92, 95, 97, 100, 103, 105, 108, 110, 113, 116, 118, 121, 124, 126, 129, 131, 134, 137, 139, 142, 144
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OFFSET
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0,2
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COMMENTS
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a(n) = greatest k such that s(k) = n+1, where s = A026350.
Indices at which blocks (0;1) occur in infinite Fibonacci word; i.e., n such that A005614(n)=0 and A005614(n+1)=1. - Benoit Cloitre, Nov 15 2003
Except for the first term, these are the numbers whose lazy Fibonacci representation (see A095791) includes both 1 and 2; thus this sequence is a subsequence of the lower Wythoff sequence, A000201. - Clark Kimberling, Jun 10 2004 [A-number typo corrected by Nathan Fox, May 03 2014]
a(n) = n-th number k whose lazy Fibonacci representation (as in A095791) has more summands than that of k-1. - Clark Kimberling, Jun 12 2004
Maximum number of chips in a pile created at each step in the game described by Roland Schroeder in his comment at A000201. (From Allan C. Wechsler via Seqfan.)
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LINKS
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MATHEMATICA
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Table[Floor[GoldenRatio*n]+n+1, {n, 0, 60}] (* Harvey P. Dale, Aug 24 2021 *)
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PROG
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(PARI) a(n) = floor(n*(sqrt(5)+1)/2) + n + 1; \\ Michel Marcus, Sep 15 2016
(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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