A275773 Primes p congruent to 1 modulo 13 such that x^13 = 2 has a solution modulo p.

4421, 4733, 5669, 5981, 8581, 9413, 10453, 11597, 13963, 14327, 14951, 19267, 22699, 22907, 23557, 25117, 25819, 26417, 28627, 31799, 32579, 35491, 37441, 41549, 44773, 44851, 45553, 46619, 46957, 48179, 49297, 49921, 49999, 50207, 52859, 53639, 60217, 64403

Offset

1,1

Comments

Intersection of A049545 and A268753.

These are the counterexamples mentioned in the Sep 12 2012 comment from Bruno Berselli in A059245.

Links

Table of n, a(n) for n=1..38.

Example

4421 is in the sequence since it is prime, it is congruent to 1 (mod 13), and x^13 == 2 (mod 4421) has the solution x = 162. - Michael B. Porter, Aug 26 2016

Mathematica

Quiet@ Select[Prime@ Range[10^4], And[Mod[#, 13] == 1, IntegerQ@ PowerMod[2, 1/13, #]] &] (* Michael De Vlieger, Aug 10 2016 *)

Prog

(PARI) forprime(p=1, 1e6, if(Mod(p, 13)==1 && ispower(Mod(2, p), 13), print1(p, ", ")))

Crossrefs

Cf. A049545, A059245, A268753.

Sequence in context: A116342 A035784 A108008 * A060363 A128194 A184091

Adjacent sequences: A275770 A275771 A275772 * A275774 A275775 A275776

Keyword

nonn

Author

Felix Fröhlich, Aug 08 2016

Status

approved