A359436 Primes p such that (4^p - 2^p + 1)/3 is prime.

3, 5, 7, 13, 29, 61, 383, 401, 1637, 1871, 36229, 44771, 44797, 75167

Offset: 1

Author

Jorge Coveiro, Dec 31 2022

Keywords

• nonn
• more
• hard

Comments

Terms > 1871 correspond to probable primes.

Is 9 the only composite k such that (4^k - 2^k + 1)/3 is prime? Checked up to 20000. - Andrew Howroyd, Sep 10 2024

Examples

			3 is a term because 3 is prime and (4^3 - 2^3 + 1)/3 = 19 is also prime.
		

Crossrefs

Cf. A000978.

Programs

PARI

isok(k)={k%2 && ispseudoprime((4^k - 2^k + 1)/3)}
{ forprime(p=3, 2000, if(isok(p), print1(p, ", "))) } \\ Andrew Howroyd, Dec 31 2022