A206713 Number of solutions (n,k) of s(k)=s(n) (mod n), where 1<=k<n and s(k)=A000045(k+1) (Fibonacci numbers).

0, 0, 1, 1, 1, 0, 1, 1, 0, 3, 2, 1, 1, 0, 1, 1, 1, 3, 0, 1, 3, 0, 2, 1, 1, 1, 2, 6, 0, 3, 5, 0, 2, 0, 4, 1, 4, 1, 2, 4, 3, 0, 1, 2, 2, 2, 5, 2, 0, 1, 2, 1, 1, 2, 2, 0, 5, 3, 2, 4, 4, 2, 2, 1, 4, 0, 3, 1, 1, 3, 8, 1, 1, 0, 8, 1, 2, 3, 2, 3, 3, 0, 6, 1, 1, 3, 6, 8, 1, 0, 3, 3, 6, 0, 5, 1, 0, 1, 1

Offset

2,10

Links

Table of n, a(n) for n=2..100.

Example

s(11)=144 = A000045(12); the numbers s(j) for j<11 are 143,142,141,139,136,131,110,89,55,
of which three are multiples of 3, so that a(11)=3.

Mathematica

s[k_] := Fibonacci[k + 1];
f[n_, k_] := If[Mod[s[n] - s[k], n] == 0, 1, 0];
t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]
a[n_] := Count[Flatten[t[n]], 1]
Table[a[n], {n, 2, 120}]  (* A206713 *)

Crossrefs

Sequence in context: A113081 A172184 A109865 * A096874 A090046 A202551

Adjacent sequences: A206710 A206711 A206712 * A206714 A206715 A206716

Keyword

nonn

Author

Clark Kimberling, Feb 11 2012

Status

approved