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A120613
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a(n) = floor(phi*floor(n/phi)) where phi=(1+sqrt(5))/2.
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4
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0, 1, 1, 3, 4, 4, 6, 6, 8, 9, 9, 11, 12, 12, 14, 14, 16, 17, 17, 19, 19, 21, 22, 22, 24, 25, 25, 27, 27, 29, 30, 30, 32, 33, 33, 35, 35, 37, 38, 38, 40, 40, 42, 43, 43, 45, 46, 46, 48, 48, 50, 51, 51, 53, 53, 55, 56, 56, 58, 59, 59, 61, 61, 63, 64, 64, 66, 67, 67, 69, 69, 71, 72
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OFFSET
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1,4
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LINKS
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FORMULA
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MATHEMATICA
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Table[Floor[GoldenRatio*Floor[n/GoldenRatio]], {n, 1, 100}] (* G. C. Greubel, Oct 23 2018 *)
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PROG
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(PARI) f=(1+sqrt(5))/2; a(n)=floor(f*floor(n/f))
(Magma) [Floor((1+Sqrt(5))*Floor(2*n/(1+Sqrt(5)))/2): n in [1..100]]; // G. C. Greubel, Oct 23 2018
(Python)
from math import isqrt
def A120613(n): return (m:=(n+isqrt(5*n**2)>>1)-n)+isqrt(5*m**2)>>1 # Chai Wah Wu, Aug 26 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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