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 A174711 #13 Apr 03 2023 10:36:12
%S A174711 9,55,513,6251,93313,1647087,33554433,774840979,20000000001,
%T A174711 570623341223,605750213184507,22224013651116033,875787780761718751,
%U A174711 36893488147419103233,1654480523772673528355,3956839311320627178247959
%N A174711 Composites of the form 2*n^n + 1 = A216147(n).
%C A174711 If p = n+2 is prime, then p divides 2*n^n + 1. Proof: Let p = n+2 prime. Then, according to Fermat's theorem, n^(p-1) == 1 (mod p). Because p-1 = n+1, n^(n+1) == 1 (mod p), and with n = p-2 == -2 (mod p), we obtain successively: n*n^n == 1 (mod p), -2*n^n == 1 (mod p), 2*n^n == -1 (mod p) => p divides 2*n^n + 1.
%D A174711 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976.
%D A174711 J. M. De Koninck, A. Mercier, 1001 problemes en theorie classique des nombres, Ellipses 2004, p. 52.
%D A174711 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.
%H A174711 C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=Composite">Composite Numbers</a>
%e A174711 a(2) = 9 = 3^2, a(3) = 55 = 5*11, a(4) = 513 = 3 ^ 3 * 19.
%p A174711 with(numtheory):for n from 0 to 50 do: x:=2*n^n + 1 : if type(x,prime)=false then print (x):else fi:od:
%t A174711 Select[Table[2n^n+1,{n,20}],CompositeQ] (* _Harvey P. Dale_, Jun 21 2015 *)
%Y A174711 Complement of A216148 in A216147. - _M. F. Hasler_, Sep 02 2012
%K A174711 nonn
%O A174711 1,1
%A A174711 _Michel Lagneau_, Mar 27 2010