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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A000040, A106483, A213078.

Sequence in context: A212604 A316934 A052354 * A260173 A321151 A052376

Adjacent sequences: A213076 A213077 A213078 * A213080 A213081 A213082

Keyword

nonn,easy

Author

Zak Seidov, Jun 04 2012

Status

approved