A105451 Numbers k such that prime(k+1) == 8 (mod k).

1, 5, 15, 73, 75, 100347, 637329, 27067271, 179993015, 1208198523, 55762149023, 55762149103, 382465573515

Offset: 1

Author

Zak Seidov, May 02 2005

Keywords

• nonn
• more
• changed

Comments

No additional terms up to 7 million. - Harvey P. Dale, Jan 23 2012

Integers k such that A004649(k+1) = 8. - Michel Marcus, Dec 30 2022

Crossrefs

Cf. A004649, A105286, A105287, A105288, A105290, A105329.

Cf. A023150 (Numbers k such that prime(n) == 8 (mod k)).

Programs

Mathematica

bb={};Do[If[8==Mod[Prime[n+1], n], bb=Append[bb, n]], {n, 1, 1000000}];bb
Select[Range[700000],Mod[Prime[#+1],#]==8&] (* Harvey P. Dale, Jan 23 2012 *)

Python

from sympy import nextprime
def A105451(max):
    terms = []
    p = 3
    for n in range(1, max+1):
        if (p - 8) % n == 0: terms.append(n)
        p = nextprime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

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

a(8)-a(10) from Michel Marcus, Dec 29 2022

a(11)-a(13) from Max Alekseyev, Aug 31 2024