A374912 Primes p such that (p - 1)^p == p (mod 2*p - 1).

3, 7, 19, 31, 79, 139, 199, 211, 271, 307, 331, 367, 379, 439, 499, 547, 607, 619, 691, 727, 811, 967, 1171, 1279, 1399, 1459, 1531, 1627, 1759, 1867, 2011, 2131, 2179, 2311, 2467, 2539, 2551, 2707, 2719, 2791, 2851, 3019, 3067, 3187, 3319, 3331, 3391, 3499, 3607, 3739, 3967

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 23 2024

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Aside from the first term, a subsequence of A068229.

Cf. A374913, A374914.

Programs

Magma

[p: p in PrimesUpTo(10^4) | (p-1)^p mod (2*p-1) eq p];

Mathematica

Select[Prime[Range[1000]], PowerMod[# - 1, #, 2*# - 1] == # &] (* Paolo Xausa, Jul 24 2024 *)

PARI

list(lim)=my(v=List([3])); forprimestep(p=7,lim\1,12, if(Mod(p-1,2*p-1)^p==p, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jul 23 2024

Formula

a(n) == 7 (mod 12) for n>1. - Hugo Pfoertner, Jul 24 2024