A105421 Numbers k such that prime(k + 1) == 7 (mod k).

1, 2, 3, 4, 8, 30, 31, 33, 68, 72, 180, 1052, 6471, 40083, 40087, 40090, 40113, 40120, 100348, 100360, 100362, 637334, 4124588, 10553439, 10553442, 10553455, 10553478, 10553505, 10553512, 10553827, 10553849, 69709712, 69709719, 69709728, 69709958, 21338685404, 1003652347332, 1003652347349, 1003652347360, 1003652347365

Offset: 1

Author

Zak Seidov, May 02 2005

Keywords

• nonn
• changed

Links

• Manfred Scheucher, Sage Script.

Crossrefs

Cf. A105286, A105287, A105288, A105290, A105329, A105451.

Programs

Mathematica

Select[Range[650000],Mod[Prime[#+1]-7,#]==0&] (* Harvey P. Dale, Sep 23 2021 *)

PARI

isok(n) = Mod(prime(n + 1), n) == Mod(7, n); \\ Michel Marcus, Apr 05 2015

PARI

n=0;forprime(p=3,,if(Mod(p,n++)==7,print1(n", "))) \\ Charles R Greathouse IV, Jul 23 2015

Python

from sympy import nextprime
def A105421(max):
    terms = []
    p = 3
    for n in range(1, max+1):
        if (p - 7) % n == 0: terms.append(n)
        p = nextprime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

a(1)-a(4) inserted by Eric M. Schmidt, Feb 05 2013

a(19)-a(22) from Harvey P. Dale, Apr 05 2015

a(23)-a(35) from Manfred Scheucher, Jul 23 2015

a(36) from Charles R Greathouse IV, Jul 23 2015

a(37)-a(40) from Max Alekseyev, Aug 31 2024