

A268753


Primes congruent to 1 mod 13.


4



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
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OFFSET

1,1


COMMENTS

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


LINKS

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


FORMULA

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


EXAMPLE

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


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A059245 (x^13 = 2 has no solution mod prime p).
Sequence in context: A129257 A125875 A059245 * A125876 A136065 A234102
Adjacent sequences: A268750 A268751 A268752 * A268754 A268755 A268756


KEYWORD

nonn,easy


AUTHOR

Alexei Kourbatov, Feb 12 2016


STATUS

approved



