A116658 Numbers k such that prime(k) == 13 (mod k).

1, 2, 6, 12, 22, 40, 42, 84, 86, 90, 193, 2712, 16056, 16058, 40077, 40123, 40124, 40125, 251720, 251766, 251769, 251787, 637332, 10553432, 10553435, 10553501, 10553568, 10553817, 10553826, 27067042, 27067132, 69709722, 179993160, 465769803

Offset: 1

Author

Zak Seidov, Feb 21 2006

Keywords

• nonn

Comments

Starting with a(5), positions of 13 in A004648. - corrected by Eric M. Schmidt, Feb 05 2013

Crossrefs

Cf. A004648; A023143 - A023152, A116657, A116677, A116658, A116659: prime(n) == m (mod n), m=1..14.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 13, Print[n]], {n, 10^9}] (* Robert G. Wilson v, Feb 22 2006 *)

Sage

def A116658(max) :
    terms = []
    p = 2
    for n in range(1, max+1) :
        if (p - 13) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

a(24)-a(34) from Robert G. Wilson v, Feb 22 2006

First four terms inserted by Eric M. Schmidt, Feb 05 2013