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Primes congruent to 2 mod 39.
5

%I #22 Sep 08 2022 08:45:35

%S 2,41,197,353,431,509,587,743,821,977,1289,1367,1523,1601,1913,2069,

%T 2381,2459,2693,2927,3083,3863,4019,4253,4409,4643,4721,4799,4877,

%U 5189,5501,5657,5813,6047,6203,6359,6827,6983,7451,7529,7607,7841,7919,8231,8387

%N Primes congruent to 2 mod 39.

%C 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

%H Vincenzo Librandi, <a href="/A142160/b142160.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ 24n log n. - _Charles R Greathouse IV_, Jul 03 2016

%t Select[Prime[Range[3000]],MemberQ[{2},Mod[#,39]]&] (* _Vincenzo Librandi_, Aug 19 2012 *)

%t Select[Range[2,9000,39],PrimeQ] (* _Harvey P. Dale_, Oct 21 2014 *)

%o (Magma)[p: p in PrimesUpTo(9000) | p mod 39 eq 2 ]; // _Vincenzo Librandi_, Aug 19 2012

%o (PARI) is(n)=isprime(n) && n%39==2 \\ _Charles R Greathouse IV_, Jul 03 2016

%Y Cf. A000040.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Jul 11 2008