cp's OEIS Frontend

A206588 Number of solutions k of prime(k)=prime(n) (mod n), where 1<=k

%I A206588 #10 Mar 30 2012 18:58:12
%S A206588 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 A206588 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 A206588 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 A206588 Number of solutions k of prime(k)=prime(n) (mod n), where 1<=k<n.
%C A206588 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 A206588 s(n).............c(n)
%C A206588 prime(n).........A206588
%C A206588 prime(n+1).......A206589
%C A206588 n^2..............A057918
%C A206588 n^3..............A206590
%C A206588 Fibonacci(n+1)...A206713
%C A206588 2^(n-1)..........A206714
%C A206588 n!...............A072480
%C A206588 n(n+1)/2.........A206824
%C A206588 n^4..............A206825
%C A206588 n(n+1)(n+2)/6....A206826
%C A206588 n(n+1)(2n+1)/6...A206827
%C A206588 C(2n,n)..........A206828
%C A206588 For some choices of s, the limiting frequency of 0's in c appears to be a positive constant.
%e A206588 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 A206588 f[n_, k_] := If[Mod[Prime[n] - Prime[k], n] == 0, 1, 0];
%t A206588 t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]
%t A206588 a[n_] := Count[Flatten[t[n]], 1]
%t A206588 Table[a[n], {n, 2, 120}]  (* A206588 *)
%Y A206588 Cf. A206589.
%K A206588 nonn
%O A206588 2,7
%A A206588 _Clark Kimberling_, Feb 09 2012