A071522 Numbers n such that x^n + x^(n-1) + x^(n-2) + ... + x + 1 is irreducible over GF(5).

1, 2, 6, 16, 22, 36, 42, 46, 52, 72, 82, 96, 102, 106, 112, 136, 156, 166, 172, 192, 196, 222, 226, 232, 256, 262, 276, 282, 292, 306, 316, 346, 352, 372, 382, 396, 432, 442, 462, 466, 502, 522, 546, 556, 562, 576, 586, 592, 606, 612, 616, 646, 652, 672, 676

Offset: 1

Author

Robert G. Wilson v, Jun 22 2002

Keywords

• easy
• nonn

Comments

Numbers k = p - 1 such that p is a prime with primitive root 5. - Joerg Arndt, Jun 25 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071642. Contained in A006093.

Programs

Maple

filter:= proc(n)
isprime(n+1) and numtheory:-order(5,n+1)=n
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 25 2020

Mathematica

Select[Prime[Range[1000]], MultiplicativeOrder[5, #] == # - 1&] - 1 (* Jean-François Alcover, Aug 16 2020 *)

PARI

forprime(p=2, 10^3, if(p==5,next()); if(znorder(Mod(5,p))==p-1, print1(p-1,", "))); \\ Joerg Arndt, Jun 25 2020

Formula

a(n) = A019335(n) - 1. - Joerg Arndt, Jun 25 2020

Extensions

a(1)=1 inserted by Robert Israel, Jun 24 2020