A376605 Primes p such that if q and r are the next two primes, (p - 1)^2 + 1, (q - 1)^2 + 1 and (r - 1)^2 + 1 are all prime.

2, 3, 5, 241, 5077, 17317, 50207, 55487, 63977, 82021, 90007, 118927, 141961, 183577, 185551, 191227, 209401, 218521, 267667, 296017, 312107, 324991, 331127, 337861, 363901, 429161, 502217, 538127, 540901, 544837, 567067, 593707, 593711, 669551, 694357, 722411, 731261, 881407, 937511, 969457

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..5000

Formula

a(n) = A000040(A376522(n)).

Example

a(4) = 241 is a term because the next two primes are 251 and 257, and (241-1)^2 + 1 = 57601, (251-1)^2 + 1 = 62501, and (257-1)^2 + 1 = 65537 are all prime.

Maple

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
J:= select(i -> isprime((P[i]-1)^2+1), [$1..nops(P)]):
P[J[select(i -> J[i+2]=J[i]+2, [$1..nops(J)-2])]];

Prog

(PARI) isok(p) = my(q=nextprime(p+1), r=nextprime(q+1)); isprime((p-1)^2+1) && isprime((q-1)^2+1) && isprime((r-1)^2+1); \\ Michel Marcus, Sep 30 2024

Crossrefs

Cf. A000040, A376522.

Sequence in context: A042067 A333803 A338262 * A042579 A033090 A303371

Adjacent sequences: A376602 A376603 A376604 * A376606 A376607 A376608

Keyword

nonn

Author

Robert Israel, Sep 29 2024

Status

approved