A283745 a(n) = least m such that 1/(n+1) < f(m) < 1/n, where f(m) = fractional part of m*(golden ratio).

1, 4, 7, 2, 10, 31, 52, 18, 39, 94, 5, 60, 115, 26, 170, 81, 225, 369, 136, 280, 47, 191, 568, 335, 102, 479, 246, 623, 13, 390, 157, 1144, 534, 911, 301, 678, 1665, 68, 445, 1432, 822, 1809, 212, 2186, 589, 1576, 2563, 966, 356, 1343, 3927, 733, 3317, 1720

Offset

1,2

Comments

This is column 1 of A283738; |a(n+1)-a(n)| is a Fibonacci number for n>=1.

Links

Table of n, a(n) for n=1..54.

Mathematica

g = GoldenRatio; z = 10000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];
r[k_] := Select[Range[z], 1/(k + 1) < t[[#]] < 1/k &, 1];
Flatten[Table[r[k], {k, 1, 200}]]  (* A283745 *)

Crossrefs

Cf. A000045, A001622, A283738, A283746.

Sequence in context: A336050 A103887 A167046 * A341813 A088446 A362253

Adjacent sequences: A283742 A283743 A283744 * A283746 A283747 A283748

Keyword

nonn,easy

Author

Clark Kimberling, Mar 17 2017

Status

approved