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A348307
Primes p such that (p-1)/2, (p-2)/3, 2*p+1, 3*p+2 are all prime numbers.
0
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.
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
KEYWORD
nonn
AUTHOR
Marc Morgenegg, Oct 11 2021
EXTENSIONS
More terms from Michel Marcus, Oct 11 2021
STATUS
approved