

A275773


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


0



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
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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 FrÃ¶hlich, Aug 08 2016


STATUS

approved



