A125611 a(n) is the smallest prime p such that 7^n divides p^6 - 1.

2, 19, 19, 3449, 32261, 152617, 3294173, 3376853, 135967277, 135967277, 7909306973, 92233439147, 115385868869, 1356446145697, 56020344873707, 56020344873707, 930522055948829, 9116268492336169, 10744682090246617

Offset

1,1

Comments

a(n) is the smallest 6th root of unity (mod 7^n) that is prime. - Robert Israel, Jan 14 2024

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Wilfrid Keller and Jörg Richstein, Fermat quotients that are divisible by p, 2014. [Wayback Machine link]

Maple

f:= proc(n) local R, r, i;
  R:= sort(map(rhs@op, [msolve(x^6=1, 7^n)]));
  for i from 0 do
    for r in R do
      if isprime(7^n * i + r) then return 7^n * i + r fi
  od od;
end proc:
map(f, [$1..30]); # Robert Israel, Jan 14 2024

Prog

(PARI) \\ See A125609

Crossrefs

Cf. A125609, A125610, A125612, A125632, A125633, A125634, A125635.

Sequence in context: A038031 A229264 A132129 * A340922 A370460 A022119

Adjacent sequences: A125608 A125609 A125610 * A125612 A125613 A125614

Keyword

nonn

Author

Alexander Adamchuk, Nov 28 2006

Extensions

More terms from Ryan Propper, Jan 03 2007

More terms from Martin Fuller, Jan 11 2007

Status

approved