A268753 - OEIS

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

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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 A354915

Adjacent sequences: A268750 A268751 A268752 * A268754 A268755 A268756

KEYWORD

nonn,easy

AUTHOR

Alexei Kourbatov, Feb 12 2016

STATUS

approved