A376605 - OEIS

%I #13 Sep 30 2024 14:09:34

%S 2,3,5,241,5077,17317,50207,55487,63977,82021,90007,118927,141961,

%T 183577,185551,191227,209401,218521,267667,296017,312107,324991,

%U 331127,337861,363901,429161,502217,538127,540901,544837,567067,593707,593711,669551,694357,722411,731261,881407,937511,969457

%N 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.

%H Robert Israel, <a href="/A376605/b376605.txt">Table of n, a(n) for n = 1..5000</a>

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

%e 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.

%p P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):

%p J:= select(i -> isprime((P[i]-1)^2+1), [$1..nops(P)]):

%p P[J[select(i -> J[i+2]=J[i]+2, [$1..nops(J)-2])]];

%o (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

%Y Cf. A000040, A376522.

%K nonn

%O 1,1

%A _Robert Israel_, Sep 29 2024