A105329 Numbers k such that prime(k+1) == 5 (mod k).

1, 2, 6, 7, 12, 14, 181, 1053, 1057, 2614, 40089, 40114, 40117, 40119, 100346, 100352, 100358, 251707, 251742, 251743, 251754, 251757, 1617173, 4124458, 10553513, 27067262, 27067272, 179992922, 179992932, 179993012, 179993172, 3140421806, 3140421838, 3140421866, 3140421872, 55762149076, 145935689366

Offset: 1

Author

Zak Seidov, Apr 30 2005

Keywords

• nonn

Comments

There are no further terms up to 215000000. - Farideh Firoozbakht, May 13 2005

Integers k such that A004649(k+1) = 5. - Michel Marcus, Dec 30 2022

Crossrefs

Cf. A004649, A105286, A105287, A105288, A105290, A105451.

Programs

Mathematica

Do[If[5 == Mod[Prime[n + 1], n], bb = Append[bb, n]], {n, 1, 251758}];
bb={};Do[If[5 == Mod[Prime[n + 1], n], bb = Append[bb, n]], {n, 1, 251758}];bb  (* Farideh Firoozbakht, May 13 2005 *)

Sage

def A105329(max) :
    terms = []
    p = 3
    for n in range(1, max+1) :
        if (p - 5) % n == 0 : terms.append(n)
        p = next_prime(p)
    return terms
# Eric M. Schmidt, Feb 05 2013

Extensions

More terms from Farideh Firoozbakht, May 13 2005

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

a(28)-a(29) corrected, a(30)-a(37) added by Max Alekseyev, Aug 31 2024