A247862 - OEIS

%I #13 Feb 16 2024 14:35:27

%S 3,5,67,395407,703903,753583,874373,1280417,1386977,2920543,3459487,

%T 3697927,3905527,4384543,4524427,5630503,6289343,6379517,7882873,

%U 8599993,8805653

%N Primes p that generate the prime quadruplets p^3-4p+2k (for k = -2, -1, 1, 2).

%e 5^3-4*5-4=101, 5^3-4*5-2=103, 5^3-4*5+2=107, 5^3-4*5+4=109 is a prime quadruplet, so 5 is in the sequence.

%t Select[Prime[Range[600000]],AllTrue[#^3-4#+2{-2,-1,1,2},PrimeQ]&] (* _Harvey P. Dale_, Feb 16 2024 *)

%o (PARI) lista(nn) = {forprime(p=2, nn, pp = p^3-4*p; if (isprime(pp-4) && isprime(pp-2) && isprime(pp+2) && isprime(pp+4), print1(p, ", ")););} \\ _Michel Marcus_, Oct 10 2014

%Y Cf. A247863.

%K nonn,more

%O 1,1

%A _Ray G. Opao_, Sep 25 2014

%E a(8)-a(21) from _Michel Marcus_, Oct 10 2014