A348307 - OEIS

%I #22 Oct 25 2021 13:27:37

%S 23,21383,26459,28643,111263,137339,217643,333563,342599,423323,

%T 486023,540539,548519,567719,658943,671039,755663,829463,865499,

%U 890063,903803,976883,1108259,1168523,1199183,1308383,1316699,1318379,1342403,1349423,1390199,1501583,1503059,1558079,1563119

%N Primes p such that (p-1)/2, (p-2)/3, 2*p+1, 3*p+2 are all prime numbers.

%C For (p-1)/2, those are the safe primes A005385.

%e 23 is a term because: (23-1)/2 = 11, (23-2)/3 = 7, 2*23+1 = 47, 3*23+2 = 71, {23, 11, 7, 47, 71} are all prime numbers.

%t Select[Range[1, 1.5*10^6, 2], AllTrue[{#, (# - 1)/2, (# - 2)/3, 2*# + 1, 3*# + 2}, PrimeQ] &] (* _Amiram Eldar_, Oct 11 2021 *)

%o (PARI) isok(p) = iferr(isprime(p) && isprime((p-1)/2) && isprime((p-2)/3) && isprime(2*p+1) && isprime(3*p+2), E, 0); \\ _Michel Marcus_, Oct 11 2021

%Y Cf. A005385 (safe primes).

%Y Intersection of A005385 and A094524 and A005384 and A023208.

%K nonn

%O 1,1

%A _Marc Morgenegg_, Oct 11 2021

%E More terms from _Michel Marcus_, Oct 11 2021