A213079 Primes p such that 2p^2-1, 3p^2-2 and 4p^2-3 are also prime.

409, 941, 6299, 10459, 11131, 11551, 15581, 16831, 17321, 17569, 25771, 25969, 26701, 31511, 36131, 40529, 43781, 50231, 52879, 54631, 54779, 56711, 60271, 61331, 70321, 71081, 83101, 83299, 85931, 100649, 110681, 116381, 118409, 118751, 120641, 130469

Offset: 1

Author

Zak Seidov, Jun 04 2012

Keywords

• nonn
• easy

Comments

Subsequence of A213078:

a(1) = 409 = A213078(4) = A106483(29) = A000040(80),

a(2) = 941 = A213078(7) = A106483(50) = A000040(160).

Links

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

Crossrefs

Cf. A000040, A106483, A213078.

Programs

Magma

[p: p in PrimesUpTo(140000) | IsPrime(2*p^2-1) and IsPrime(3*p^2-2) and IsPrime(4*p^2-3)]; // Vincenzo Librandi, Apr 08 2013

Mathematica

Select[Prime[Range[20000]], PrimeQ[2 #^2 - 1] && PrimeQ[3 #^2 - 2] && PrimeQ[4 #^2 - 3] &] (* T. D. Noe, Jun 06 2012 *)
Select[Prime[Range[12500]],AllTrue[{2#^2-1,3#^2-2,4#^2-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 11 2015 *)