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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.

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

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%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