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A160021 a(n)=2^(2^n)+33, Fermat numbers of order 33. 1

%I

%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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Last modified May 21 15:12 EDT 2019. Contains 323444 sequences. (Running on oeis4.)