A268753 Primes congruent to 1 mod 13.

53, 79, 131, 157, 313, 443, 521, 547, 599, 677, 859, 911, 937, 1093, 1171, 1223, 1249, 1301, 1327, 1483, 1613, 1847, 1873, 1951, 2003, 2029, 2081, 2237, 2341, 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

Offset: 1

Author

Alexei Kourbatov, Feb 12 2016

Keywords

• nonn
• easy

Comments

The first 45 terms, up to 4057, coincide with A059245. Then a(46)=4421 occurs in this sequence, while A059245(46)=4447.

Examples

			53 is the first prime of the form 13k + 1, therefore a(1)=53.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A059245 (x^13 = 2 has no solution mod prime p).

Programs

Magma

[p: p in PrimesUpTo(5300) | p mod 13 in {1} ]; // Vincenzo Librandi, Feb 13 2016

Mathematica

Select[Prime@ Range@ 700, Mod[#, 13] == 1 &] (* Michael De Vlieger, Feb 12 2016 *)

PARI

forprime(p=2, 1e4, if(p%13==1, print1(p", ")))

PARI

forprimestep(p=53,1e4,26,print1(p", ")) \\ Charles R Greathouse IV, Mar 11 2020

Formula

a(n) ~ 12n log n. - Charles R Greathouse IV, Mar 11 2020