A126032 Numbers of the form b^m/2 for even b and odd m > 2.

4, 16, 32, 64, 108, 256, 500, 512, 864, 1024, 1372, 2048, 2916, 3888, 4000, 4096, 5324, 6912, 8192, 8788, 10976, 13500, 16384, 19652, 23328, 27436, 32000, 37044, 42592, 48668, 50000, 55296, 62500, 65536, 70304, 78732, 87808, 97556, 108000, 119164, 124416

Offset

1,1

Comments

The old definition was: Numbers n such that A123669(n) = -1, or no generalized Fermat prime exists of the form (2n)^(2^k) + 1. But that sequence is probably missing a lot of terms, such as {6, 9, 11, 19, 21, 25, 26, 29, 30, 31, ...}, where no generalized Fermat prime has been found yet, and it seems unlikely any exist. Currently it can only be proved that none exist if n is of form b^m/2 for even b and odd m > 1. The listed terms are the first numbers of this form: 4 = 2^3/2, 16 = 2^5/2, 32 = 4^3/2, 64 = 2^7/2, 108 = 6^3/2, 256 = 2^9/2 = 8^3/2, 500 = 10^3/2. - Jens Kruse Andersen, Jul 24 2014

The even terms of A070265, divided by two. - Jeppe Stig Nielsen, Jul 02 2017

Links

Table of n, a(n) for n=1..41.

Jeppe Stig Nielsen, Generalized Fermat Primes sorted by base.

Eric Weisstein's World of Mathematics, Generalized Fermat Number.

Mathematica

Module[{nn = 2^17, a = {}, n}, Do[If[b > nn, Break[], Do[If[Set[n, b^m/2] > nn, Break[], AppendTo[a, n]], {m, 3, Infinity, 2}]], {b, 2, Infinity, 2}]; Union@ a] (* Michael De Vlieger, Jul 04 2017 *)

Prog

(PARI) isOK(n)=ip=ispower(2*n); ip&&bitand(ip, ip-1) \\ Jeppe Stig Nielsen, Jul 02 2017

Crossrefs

Cf. A123669 = Smallest generalized Fermat prime of the form (2n)^(2^k) + 1, where k>0.

Cf. A070265.

Sequence in context: A243980 A119677 A326873 * A296819 A034713 A101653

Adjacent sequences: A126029 A126030 A126031 * A126033 A126034 A126035

Keyword

easy,nonn

Author

Alexander Adamchuk, Feb 28 2007

Extensions

Definition changed by N. J. A. Sloane, Jul 26 2014 following the advice of Jens Kruse Andersen.

Terms after a(7) from Jeppe Stig Nielsen, Jul 02 2017

Status

approved