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

1, 2, 3, 5, 143, 225

Offset

1,2

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

Links

Table of n, a(n) for n=1..6.

Example

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.

Maple

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

Prog

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

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.

Sequence in context: A117702 A041343 A229349 * A325505 A366642 A319609

Adjacent sequences: A160597 A160598 A160599 * A160601 A160602 A160603

Keyword

hard,more,nonn

Author

M. F. Hasler, Jul 10 2009

Status

approved