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

35, 37, 49, 289, 65569, 4294967329, 18446744073709551649, 340282366920938463463374607431768211489, 115792089237316195423570985008687907853269984665640564039457584007913129639969

Offset: 1

Author

Cino Hilliard, Apr 30 2009

Keywords

• nonn

Comments

Fermat numbers of order m are defined by F(n,m) = 2^(2^n)+m = A001146(n)+m.

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.)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..12
• Cino Hilliard, Fermat numbers of order m

Crossrefs

Cf. A130730 (order 7).

Programs

Magma

[2^(2^n)+33: n in [0..11]]; // Vincenzo Librandi, Jan 09 2013

Mathematica

Table[(2^(2^n) + 33), {n, 0, 15}] (* Vincenzo Librandi, Jan 09 2013 *)

PARI

g(n) = for(x=0,n,y=2^(2^x)+33;print1(y","))

Extensions

Edited by R. J. Mathar, May 08 2009