A374914 Primes p == 2, 3 (mod 4) with 2*p+1 prime.

2, 3, 11, 23, 83, 131, 179, 191, 239, 251, 359, 419, 431, 443, 491, 659, 683, 719, 743, 911, 1019, 1031, 1103, 1223, 1439, 1451, 1499, 1511, 1559, 1583, 1811, 1931, 2003, 2039, 2063, 2339, 2351, 2399, 2459, 2543, 2699, 2819, 2903, 2939, 2963, 3023, 3299, 3359, 3491

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 23 2024

Keywords

• nonn
• easy

Comments

2 together with Lucasian primes (A002515).

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

Examples

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

Crossrefs

Supersequence of A002515. Subsequence of A374913.

Cf. A374912.

Programs

Mathematica

Select[Prime[Range[490]],Mod[#^(#+1),2#+1]==#+1 &] (* Stefano Spezia, Jul 23 2024 *)

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

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Jul 25 2024