A283746 a(n) = least m such that (n-1)/n < f(m) < n/(n+1), where f(m) = fractional part of m*(golden ratio).

2, 1, 6, 11, 24, 3, 37, 16, 105, 50, 84, 29, 118, 207, 63, 152, 8, 241, 97, 330, 186, 419, 42, 275, 508, 131, 741, 364, 597, 220, 830, 453, 76, 686, 1296, 309, 919, 1529, 542, 165, 1762, 775, 1385, 398, 1008, 21, 1618, 631, 2228, 1241, 254, 1851, 864, 2461

Offset

1,1

Comments

This is column 1 of A283739; |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], (k - 1)/k < t[[#]] < k/(k + 1) &, 1];
Flatten[Table[r[k], {k, 1, 200}]]  (* A283746 *)

Crossrefs

Cf. A000045, A001622, A283739, A283745.

Sequence in context: A200265 A039762 A039795 * A049949 A106192 A113025

Adjacent sequences: A283743 A283744 A283745 * A283747 A283748 A283749

Keyword

nonn,easy

Author

Clark Kimberling, Mar 17 2017

Status

approved