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A160021 a(n)=2^(2^n)+33, Fermat numbers of order 33. 1
35, 37, 49, 289, 65569, 4294967329, 18446744073709551649, 340282366920938463463374607431768211489, 115792089237316195423570985008687907853269984665640564039457584007913129639969 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

Cf. A130730 (order 7).

Sequence in context: A064993 A041611 A160775 * A172016 A064610 A030589

Adjacent sequences:  A160018 A160019 A160020 * A160022 A160023 A160024

KEYWORD

nonn

AUTHOR

Cino Hilliard, Apr 30 2009

EXTENSIONS

Edited by R. J. Mathar, May 08 2009

STATUS

approved

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Last modified April 26 04:37 EDT 2019. Contains 322469 sequences. (Running on oeis4.)