A245045 Primes of the form (k^2+2)/6.

3, 11, 17, 43, 67, 113, 131, 193, 241, 353, 523, 641, 683, 1291, 1601, 1667, 1873, 2017, 2243, 2731, 3083, 3361, 3851, 4483, 4817, 4931, 5281, 5521, 7211, 8363, 8513, 8971, 9283, 9923, 10753, 11971, 13633, 16433, 17713, 18371, 18593, 19267, 21841, 22571

Offset: 1

Author

Chai Wah Wu, Jul 10 2014

Keywords

• nonn

Examples

			When k=4, (k^2+2)/6 = 3 is prime, so 4 is a member of the sequence. since putting k = 0, 1, 2, or 3 does not give a prime, so 4 is the first term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A154616, A002327, A066436. First 5 terms equal to A078116. First 4 terms equal to A127996.

Programs

Python

import sympy
[(k**2+2)/6 for k in range(10**6) if sympy.ntheory.isprime((k**2+2)/6) & ((k**2+2)/6).is_integer()]