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%I #23 Apr 03 2023 10:36:13
%S 3,17832200896513,78692816150593075150849
%N Primes of the form 2*k^k + 1 = A216147(k).
%C The sequence should be extended through A110932, which lists the corresponding values of k: The next term, 2*251^251 + 1 = A216147(A110932(4)) ~ 4.16*10^602, is too large to include here.
%H M. F. Hasler, <a href="/A216148/b216148.txt">Table of n, a(n) for n = 1..4</a>
%H C. Caldwell, G.L. Honaker (Eds), <a href="https://t5k.org/curios/page.php/78692816150593075150849.html">Prime Curios!: 78692816150593075150849</a>.
%H "Jim", <a href="http://mathforum.org/kb/message.jspa?messageID=544888">Topic: The Lost Proof of Fermat</a>, on mathforum.org, Jan 31 2004
%F a(2) = A216147(12) = A005109(95) = A070855(12) = A058383(89) = A133663(18).
%F a(3) = A216147(18) = A005109(183)= A070855(18) = A058383(177)= A133663(36).
%t Select[Table[2n^n+1,{n,20}],PrimeQ] (* _Harvey P. Dale_, Mar 27 2016 *)
%o (PARI) for(n=1,999, ispseudoprime(p=n^n*2+1) & print1(p","))
%Y Cf. A110932.
%Y A subsequence of A133663, with b=a and c=1.
%K nonn,bref,less
%O 1,1
%A _M. F. Hasler_, Sep 02 2012