A049596 - OEIS

A049596

Primes p such that x^9 = 2 has a solution mod p.

2, 3, 5, 11, 17, 23, 29, 31, 41, 43, 47, 53, 59, 71, 83, 89, 101, 107, 113, 127, 131, 137, 149, 157, 167, 173, 179, 191, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 277, 281, 283, 293, 311, 317, 347, 353, 359, 383, 389, 397, 401, 419, 431, 439, 443, 449

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OFFSET

1,1

COMMENTS

Coincides with sequence of "primes p such that x^27 = 2 has a solution mod p" for first 339 terms, then diverges.

Complement of A059262 relative to A000040. - Vincenzo Librandi, Sep 15 2012

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000

Index entries for related sequences

EXAMPLE

0^9 == 2 (mod 2). 2^9 == 2 (mod 3). 2^9 == 2 (mod 5). 6^9 == 2 (mod 11). 2^9 == 2 (mod 17). 9^9 == 2 (mod 23). 11^9 == 2 (mod 29). 16^9 == 2 (mod 31). 20^9 == 2 (mod 41). 26^9 == 2 (mod 43). - R. J. Mathar, Jul 20 2025

MATHEMATICA

ok[p_]:= Reduce[Mod[x^9 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

PROG

(Magma) [p: p in PrimesUpTo(500) | exists(t){x : x in ResidueClassRing(p) | x^9 eq 2}]; // Vincenzo Librandi, Sep 15 2012

CROSSREFS

Cf. A000040, A001132, A059262.

Sequence in context: A040028 A049589 A049583 * A049571 A263090 A098058

Adjacent sequences: A049593 A049594 A049595 * A049597 A049598 A049599

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved