A214053 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.

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

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

floor(4*r) = A000201(4) = 6; gcd(6+1,4-1) = 1 and gcd(6+2,4-2) = 2, so a(4) = 2.

Mathematica

a[n_] := NestWhile[# + 1 &, 1, CoprimeQ[Floor[GoldenRatio*n] + #, n - #] &] (* Sidney Cadot, Feb 19 2023 *)

Crossrefs

Sequence in context: A130069 A120007 A092509 * A214056 A368900 A014973

Adjacent sequences: A214050 A214051 A214052 * A214054 A214055 A214056

Keyword

nonn,easy

Author

Clark Kimberling, Jul 21 2012

Status

approved