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%I #17 Sep 08 2022 08:45:44
%S 35,37,49,289,65569,4294967329,18446744073709551649,
%T 340282366920938463463374607431768211489,
%U 115792089237316195423570985008687907853269984665640564039457584007913129639969
%N a(n)=2^(2^n)+33, Fermat numbers of order 33.
%C Fermat numbers of order m are defined by F(n,m) = 2^(2^n)+m = A001146(n)+m.
%C F(1,33) = 37 is the only prime in this sequence. (If n is even, 7 divides F(n,33). For n > 2, 17 divides F(n,33). Proofs are in the link.)
%H Vincenzo Librandi, <a href="/A160021/b160021.txt">Table of n, a(n) for n = 1..12</a>
%H Cino Hilliard, <a href="http://groups.google.com/group/numbertheory/web/fermat-numbers-of-order-m">Fermat numbers of order m</a>
%t Table[(2^(2^n) + 33), {n, 0, 15}] (* _Vincenzo Librandi_, Jan 09 2013 *)
%o (PARI) g(n) = for(x=0,n,y=2^(2^x)+33;print1(y","))
%o (Magma) [2^(2^n)+33: n in [0..11]]; // _Vincenzo Librandi_, Jan 09 2013
%Y Cf. A130730 (order 7).
%K nonn
%O 1,1
%A _Cino Hilliard_, Apr 30 2009
%E Edited by _R. J. Mathar_, May 08 2009
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