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A026351
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a(n) = floor(n*phi) + 1, where phi = (1+sqrt(5))/2.
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24
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1, 2, 4, 5, 7, 9, 10, 12, 13, 15, 17, 18, 20, 22, 23, 25, 26, 28, 30, 31, 33, 34, 36, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 54, 56, 57, 59, 60, 62, 64, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 89, 91, 93, 94, 96, 98, 99
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OFFSET
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0,2
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COMMENTS
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a(n)=least k such that s(k)=n, where s=A026350.
a(n)=position of n-th 1 in A096270.
a(n) = A(n)+1, with Wythoff sequence A(n)=A000201(n), n>=1, and A(0)=0.
a(n) = -floor(-n*phi). Recall that floor(-x) = -(floor(x)+1) if x is not integer and -floor(x) otherwise.
An exhaustive and disjoint decomposition of the integers is given by the following two Wythoff sequences A' and B: A'(0):=-1 (not 0), A'(-n):=-a(n)=-(A(n)+1), n>=1, A'(n) = A(n), n>=1, and B(-n):=-(B(n)+1)= -A026352(n), n>=1, with B(n)=A001950(n), n>=1, and B(0)=0.
(End)
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LINKS
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MATHEMATICA
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Table[Floor[n*GoldenRatio] + 1, {n, 0, 100}] (* T. D. Noe, Apr 15 2011 *)
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PROG
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(Haskell)
import Data.List (findIndices)
a026351 n = a026351_list !! n
a026351_list = findIndices odd a060142_list
(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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