A206588 - OEIS

%I #10 Mar 30 2012 18:58:12

%S 0,1,1,0,1,1,2,1,1,0,1,1,1,2,2,0,2,1,2,1,1,1,2,1,1,0,2,0,3,1,2,2,3,1,

%T 3,1,1,2,2,1,3,1,3,2,2,1,3,1,3,2,2,1,2,1,1,1,1,1,2,0,1,1,0,1,2,1,1,2,

%U 1,1,1,1,2,2,3,0,3,0,1,1,2,0,4,1,2,1,3,1,5,1,1,0,1,0,2,0,2,1,2

%N Number of solutions k of prime(k)=prime(n) (mod n), where 1<=k<n.

%C In the following guide to related sequences, c(n) is the number of solutions (n,k) of s(k)=s(n) (mod n), where 1<=k<n.

%C s(n).............c(n)

%C prime(n).........A206588

%C prime(n+1).......A206589

%C n^2..............A057918

%C n^3..............A206590

%C Fibonacci(n+1)...A206713

%C 2^(n-1)..........A206714

%C n!...............A072480

%C n(n+1)/2.........A206824

%C n^4..............A206825

%C n(n+1)(n+2)/6....A206826

%C n(n+1)(2n+1)/6...A206827

%C C(2n,n)..........A206828

%C For some choices of s, the limiting frequency of 0's in c appears to be a positive constant.

%e For k=1 to 7, the numbers p(8)-p(k) are 17,16,14,12,8,6,4, so that a(8)=2.

%t f[n_, k_] := If[Mod[Prime[n] - Prime[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}]  (* A206588 *)

%Y Cf. A206589.

%K nonn

%O 2,7

%A _Clark Kimberling_, Feb 09 2012