This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A160600 #17 Aug 04 2025 21:20:56 %S A160600 1,2,3,5,143,225 %N A160600 Numbers k such that 3*(2k)^(2k)+1 is prime. %C A160600 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. %C A160600 Next term > 15000. - _Matevz Markovic_, Oct 09 2012 %e A160600 a(1) = 1, because 2^2*3+1 = 13 is the smallest prime of this form. %e A160600 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. %p A160600 q:= k-> isprime(3*(2*k)^(2*k)+1): %p A160600 select(q, [$1..225])[]; # _Alois P. Heinz_, Aug 04 2025 %o A160600 (PARI) for(i=1,9999,ispseudoprime(i^i*3+1)&print1(i/2,",")) %Y A160600 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. %K A160600 hard,more,nonn %O A160600 1,2 %A A160600 _M. F. Hasler_, Jul 10 2009