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%I #16 Sep 08 2022 08:46:15
%S 53,79,131,157,313,443,521,547,599,677,859,911,937,1093,1171,1223,
%T 1249,1301,1327,1483,1613,1847,1873,1951,2003,2029,2081,2237,2341,
%U 2393,2549,2731,2861,2887,2939,3121,3251,3329,3407,3433,3511,3719,3797,3823,4057,4421,4447,4603,4733,4759,4889,4967,4993,5227,5279
%N Primes congruent to 1 mod 13.
%C The first 45 terms, up to 4057, coincide with A059245. Then a(46)=4421 occurs in this sequence, while A059245(46)=4447.
%H Daniel Starodubtsev, <a href="/A268753/b268753.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ 12n log n. - _Charles R Greathouse IV_, Mar 11 2020
%e 53 is the first prime of the form 13k + 1, therefore a(1)=53.
%t Select[Prime@ Range@ 700, Mod[#, 13] == 1 &] (* _Michael De Vlieger_, Feb 12 2016 *)
%o (PARI) forprime(p=2, 1e4, if(p%13==1, print1(p", ")))
%o (PARI) forprimestep(p=53,1e4,26,print1(p", ")) \\ _Charles R Greathouse IV_, Mar 11 2020
%o (Magma) [p: p in PrimesUpTo(5300) | p mod 13 in {1} ]; // _Vincenzo Librandi_, Feb 13 2016
%Y Cf. A059245 (x^13 = 2 has no solution mod prime p).
%K nonn,easy
%O 1,1
%A _Alexei Kourbatov_, Feb 12 2016
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