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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). 2

%I #6 Mar 30 2012 18:58:12

%S 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,

%T 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,

%U 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

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

%e s(11)=144 = A000045(12); the numbers s(j) for j<11 are 143,142,141,139,136,131,110,89,55,

%e of which three are multiples of 3, so that a(11)=3.

%t s[k_] := Fibonacci[k + 1];

%t f[n_, k_] := If[Mod[s[n] - s[k], n] == 0, 1, 0];

%t t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]

%t a[n_] := Count[Flatten[t[n]], 1]

%t Table[a[n], {n, 2, 120}] (* A206713 *)

%K nonn

%O 2,10

%A _Clark Kimberling_, Feb 11 2012

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)