A229786 a(n) = n-th prime modulo 23.

2, 3, 5, 7, 11, 13, 17, 19, 0, 6, 8, 14, 18, 20, 1, 7, 13, 15, 21, 2, 4, 10, 14, 20, 5, 9, 11, 15, 17, 21, 12, 16, 22, 1, 11, 13, 19, 2, 6, 12, 18, 20, 7, 9, 13, 15, 4, 16, 20, 22, 3, 9, 11, 21, 4, 10, 16, 18, 1, 5, 7, 17, 8, 12, 14, 18, 9, 15, 2, 4, 8, 14, 22, 5, 11, 15, 21, 6, 10, 18, 5, 7, 17, 19, 2, 6, 12, 20, 1, 3, 7, 19, 4, 8, 16, 20, 3, 15, 17, 12, 18, 5, 11, 17, 19, 2, 12, 18, 1, 3, 9, 15, 19, 21

Offset: 1

Author

Freimut Marschner, Sep 29 2013

Keywords

• nonn
• easy

Comments

The formula k(n,p)=p mod n classifies prime numbers p(A000040) with n(A000027) in classes k, here n=23. Other examples for n=2,3,4,... are in the cross reference. Another description of this sequence is a(n) = n-th prime modulo 23 or Prime(n) mod 23.

Links

• Freimut Marschner, Table of n, a(n) for n = 1..1900

Crossrefs

Cf. similar sequences listed in A242119.

Programs

Magma

[p mod(23): p in PrimesUpTo(500)]; // Vincenzo Librandi, May 07 2014

Mathematica

Mod[Prime[Range[100]], 23] (* Vincenzo Librandi, May 07 2014 *)

Formula

k(n,p) = p mod n.

Sum_k={1..n} a(k) ~ (23/2)*n. - Amiram Eldar, Dec 12 2024