%I #15 Sep 08 2022 08:46:02

%S 409,941,6299,10459,11131,11551,15581,16831,17321,17569,25771,25969,

%T 26701,31511,36131,40529,43781,50231,52879,54631,54779,56711,60271,

%U 61331,70321,71081,83101,83299,85931,100649,110681,116381,118409,118751,120641,130469

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

%C Subsequence of A213078:

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

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

%H Vincenzo Librandi, <a href="/A213079/b213079.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Prime[Range[20000]], PrimeQ[2 #^2 - 1] && PrimeQ[3 #^2 - 2] && PrimeQ[4 #^2 - 3] &] (* _T. D. Noe_, Jun 06 2012 *)

%t 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 *)

%o (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

%Y Cf. A000040, A106483, A213078.

%K nonn,easy

%O 1,1

%A _Zak Seidov_, Jun 04 2012