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

1,2

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A071642. Contained in A006093.

Sequence in context: A085226 A260376 A330866 * A192532 A230853 A364666

Adjacent sequences: A071519 A071520 A071521 * A071523 A071524 A071525

Keyword

easy,nonn

Author

Robert G. Wilson v, Jun 22 2002

Extensions

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

Status

approved