A374914 - OEIS

%I #11 Jul 25 2024 14:05:58

%S 2,3,11,23,83,131,179,191,239,251,359,419,431,443,491,659,683,719,743,

%T 911,1019,1031,1103,1223,1439,1451,1499,1511,1559,1583,1811,1931,2003,

%U 2039,2063,2339,2351,2399,2459,2543,2699,2819,2903,2939,2963,3023,3299,3359,3491

%N Primes p == 2, 3 (mod 4) with 2*p+1 prime.

%C 2 together with Lucasian primes (A002515).

%C Primes p such that p^(p + 1) == p + 1 (mod 2*p + 1).

%F a(n) >> n log^2 n. - _Charles R Greathouse IV_, Jul 25 2024

%e 2 is in this sequence because 2^(2 + 1) = 8 and 8 = 3 (mod 2*2 + 1) where 2 prime.

%t Select[Prime[Range[490]],Mod[#^(#+1),2#+1]==#+1 &] (* _Stefano Spezia_, Jul 23 2024 *)

%o (PARI) list(lim)=my(v=List([2])); forprimestep(p=3,lim\1,4, if(isprime(2*p+1), listput(v,p))); Vec(v) \\ _Charles R Greathouse IV_, Jul 25 2024

%Y Supersequence of A002515. Subsequence of A374913.

%Y Cf. A374912.

%K nonn,easy

%O 1,1

%A _Juri-Stepan Gerasimov_, Jul 23 2024