A142160 Primes congruent to 2 mod 39.

2, 41, 197, 353, 431, 509, 587, 743, 821, 977, 1289, 1367, 1523, 1601, 1913, 2069, 2381, 2459, 2693, 2927, 3083, 3863, 4019, 4253, 4409, 4643, 4721, 4799, 4877, 5189, 5501, 5657, 5813, 6047, 6203, 6359, 6827, 6983, 7451, 7529, 7607, 7841, 7919, 8231, 8387

Offset: 1

Author

N. J. A. Sloane, Jul 11 2008

Keywords

• nonn
• easy

Comments

a(4)..a(7) are the first set of 4 prime-indexed primes in arithmetic progression: a(4) = 353 = prime(prime(20)); a(5) = 431 = prime(prime(23)); a(6) = 509 = prime(prime(25)); a(7) = 587 = prime(prime(28)). Then we can see that 431-353 = 509-431 = 587-509 = 78. - Bobby Jacobs, Nov 30 2016

2 and primes congruent to 41 mod 78. - Chai Wah Wu, Apr 29 2025

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040.

Programs

Magma

[p: p in PrimesUpTo(9000) | p mod 39 eq 2 ]; // Vincenzo Librandi, Aug 19 2012

Mathematica

Select[Prime[Range[3000]],MemberQ[{2},Mod[#,39]]&] (* Vincenzo Librandi, Aug 19 2012 *)
Select[Range[2,9000,39],PrimeQ] (* Harvey P. Dale, Oct 21 2014 *)

PARI

is(n)=isprime(n) && n%39==2 \\ Charles R Greathouse IV, Jul 03 2016

Formula

a(n) ~ 24n log n. - Charles R Greathouse IV, Jul 03 2016