A160600 Numbers k such that 3*(2k)^(2k)+1 is prime.

1, 2, 3, 5, 143, 225

Offset: 1

Author

M. F. Hasler, Jul 10 2009

Keywords

• hard
• more
• nonn

Comments

This corresponds to the numbers such that 3m^m+1 is prime, but these must all be even, m=2k, and therefore it is more natural to record the sequence of k=m/2.

Next term > 15000. - Matevz Markovic, Oct 09 2012

Examples

			a(1) = 1, because 2^2*3+1 = 13 is the smallest prime of this form.
a(2) = 2, because 4^4*3+1 = 769 is the next smallest prime of this form. a(3) = 3, because 6^6*3+1 = 139969 is again a prime.
		

Crossrefs

Cf. A160360 (3n^n+2 is prime), A121270 = primes among Sierpinski numbers A014566(n)=n^n+1; A216148 = A216147(A110932): primes 2n^n+1; A088790, A065798.

Programs

Maple

q:= k-> isprime(3*(2*k)^(2*k)+1):
select(q, [$1..225])[];  # Alois P. Heinz, Aug 04 2025

PARI

for(i=1,9999,ispseudoprime(i^i*3+1)&print1(i/2,","))