The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A126032 Numbers of the form b^m/2 for even b and odd m > 2. 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 (list; graph; refs; listen; history; text; internal format)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 29 01:11 EDT 2021. Contains 346340 sequences. (Running on oeis4.)