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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

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OFFSET

1,1

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

FORMULA

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

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 *)

PROG

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

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

CROSSREFS