A125609 Smallest prime p such that 3^n divides p^2 - 1.

2, 17, 53, 163, 487, 1459, 4373, 13121, 39367, 472391, 1062881, 1062881, 19131877, 19131877, 57395627, 86093443, 258280327, 3874204891, 6973568801, 6973568801, 188286357653, 188286357653, 188286357653, 4518872583697, 15251194969973

Offset

1,1

Comments

Smallest prime of the form k*3^n-1 or k*3^n+1. - Robert Israel, Oct 27 2019

Links

Robert Israel, Table of n, a(n) for n = 1..2088

Martin Fuller, PARI program

W. Keller and J. Richstein, Fermat quotients that are divisible by p.

Maple

f:= proc(n) local k;
      for k from 1 do
        if isprime(k*3^n-1) then return k*3^n-1
        elif isprime(k*3^n+1) then return k*3^n+1
        fi
      od
end proc:
map(f, [$1..30]); # Robert Israel, Oct 27 2019

Mathematica

f[n_] := Module[{k}, For[k = 1, True, k++, If[PrimeQ[k*3^n-1], Return[k*3^n-1], If[PrimeQ[k*3^n+1], Return[k*3^n+1]]]]];
Array[f, 30] (* Jean-François Alcover, Jun 04 2020, after Maple *)

Prog

For PARI program see link.

Crossrefs

Cf. A125609 = Smallest prime p such that 3^n divides p^2 - 1. Cf. A125610 = Smallest prime p such that 5^n divides p^4 - 1. Cf. A125611 = Smallest prime p such that 7^n divides p^6 - 1. Cf. A125612 = Smallest prime p such that 11^n divides p^10 - 1. Cf. A125632 = Smallest prime p such that 13^n divides p^12 - 1. Cf. A125633 = Smallest prime p such that 17^n divides p^16 - 1. Cf. A125634 = Smallest prime p such that 19^n divides p^18 - 1. Cf. A125635 = Smallest prime p such that 257^n divides p^256 - 1.

Sequence in context: A192345 A212836 A338564 * A377699 A100518 A367032

Adjacent sequences: A125606 A125607 A125608 * A125610 A125611 A125612

Keyword

nonn

Author

Alexander Adamchuk, Nov 28 2006

Extensions

Corrected and extended by Ryan Propper, Jan 01 2007

More terms from Martin Fuller, Jan 11 2007

Status

approved