A348307 Primes p such that (p-1)/2, (p-2)/3, 2*p+1, 3*p+2 are all prime numbers.

23, 21383, 26459, 28643, 111263, 137339, 217643, 333563, 342599, 423323, 486023, 540539, 548519, 567719, 658943, 671039, 755663, 829463, 865499, 890063, 903803, 976883, 1108259, 1168523, 1199183, 1308383, 1316699, 1318379, 1342403, 1349423, 1390199, 1501583, 1503059, 1558079, 1563119

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..35.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A005385 (safe primes).

Intersection of A005385 and A094524 and A005384 and A023208.

Sequence in context: A028693 A324255 A273940 * A033998 A157167 A273192

Adjacent sequences: A348304 A348305 A348306 * A348308 A348309 A348310

Keyword

nonn

Author

Marc Morgenegg, Oct 11 2021

Extensions

More terms from Michel Marcus, Oct 11 2021

Status

approved