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A214053
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Least m>0 such that floor(n*r)+m and n-m have a common divisor > 1, where r = (1+sqrt(5))/2, the golden ratio.
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1
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1, 2, 3, 2, 5, 1, 1, 2, 9, 2, 1, 12, 1, 2, 2, 16, 1, 18, 5, 2, 1, 1, 1, 2, 5, 2, 1, 28, 2, 2, 1, 32, 1, 34, 7, 2, 1, 2, 1, 1, 41, 42, 1, 4, 3, 1, 2, 3, 1, 2, 2, 1, 1, 3, 3, 2, 57, 58, 1, 60, 1, 2, 1, 64, 1, 2, 2, 2, 1, 1, 1, 2, 73, 74, 1, 1, 2, 2, 1, 3, 1, 2
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OFFSET
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1,2
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LINKS
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EXAMPLE
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floor(4*r) = A000201(4) = 6; gcd(6+1,4-1) = 1 and gcd(6+2,4-2) = 2, so a(4) = 2.
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MATHEMATICA
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a[n_] := NestWhile[# + 1 &, 1, CoprimeQ[Floor[GoldenRatio*n] + #, n - #] &] (* Sidney Cadot, Feb 19 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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