A201473 Primes of the form 2*k^2 + 3.

3, 5, 11, 53, 101, 131, 971, 1061, 1571, 2741, 3203, 3701, 4421, 5003, 6053, 7691, 9803, 13451, 13781, 16931, 19211, 21221, 22901, 24203, 25541, 27851, 31253, 32261, 32771, 35381, 51203, 57803, 61253, 69941, 77621, 81611, 82421, 84053, 86531, 89891, 122021, 125003

Offset: 1

Author

Vincenzo Librandi, Dec 02 2011

Keywords

• nonn
• easy

Comments

All numbers p satisfying: p = 2*n^2 + 3 such that 2^(n^2 + 1) == 2*n^2 + 2 (mod p). For example: a(5) = 101; 2^50 == 100 (mod 101). - Alzhekeyev Ascar M, May 27 2013

Or, primes in A093328. - Zak Seidov, Sep 27 2015

Examples

			5 is in the sequence since it is a prime and can be expressed as 2*(1^2) + 3.
11 is in the sequence since it is a prime and can be expressed as 2*(2^2) + 3.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A093328, A216968.

Programs

Magma

[a: n in [0..400] | IsPrime(a) where a is 2*n^2+3];

Mathematica

Select[Table[2n^2 + 3, {n, 0, 800}], PrimeQ]

Formula

a(n) = A093328(A216968(n)). - Elmo R. Oliveira, Apr 21 2025