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

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, 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, 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

Offset

2,7

Comments

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.

s(n).............c(n)

prime(n).........A206588

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

n^2..............A057918

n^3..............A206590

Fibonacci(n+1)...A206713

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

n!...............A072480

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

n^4..............A206825

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

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

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

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A206589.

Sequence in context: A250205 A326017 A290307 * A302234 A345007 A026920

Adjacent sequences: A206585 A206586 A206587 * A206589 A206590 A206591

Keyword

nonn

Author

Clark Kimberling, Feb 09 2012

Status

approved