login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123599 Smallest generalized Fermat prime of the form a^(2^n) + 1, where base a>1 is an integer; or -1 if no such prime exists. 6
3, 5, 17, 257, 65537, 185302018885184100000000000000000000000000000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

First 5 terms {3, 5, 17, 257, 65537} = A019434(n) are the Fermat primes of the form 2^(2^n) + 1. Note that for all currently known a(n) up to n = 17 last digit is 7 or 1 (except a(0) = 3 and a(1) = 5). Corresponding least bases a>1 such that a^(2^n) + 1 is prime are listed in A056993(n) = {2, 2, 2, 2, 2, 30, 102, 120, 278, 46, 824, 150, 1534, 30406, 67234, 70906, 48594, 62722, ...}.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..9

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

MATHEMATICA

Do[f=Min[Select[ Table[ i^(2^n) + 1, {i, 2, 500} ], PrimeQ]]; Print[{n, f}], {n, 0, 9}]

CROSSREFS

Cf. A019434 = Fermat primes of the form 2^(2^n) + 1. Cf. A000215 = Fermat numbers: 2^(2^n) + 1. Cf. A056993 = smallest k >= 2 such that k^(2^n)+1 is prime. Cf. A006093, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002.

Sequence in context: A262534 A000215 A263539 * A100270 A016045 A128336

Adjacent sequences:  A123596 A123597 A123598 * A123600 A123601 A123602

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Nov 14 2006

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified July 27 20:09 EDT 2017. Contains 289866 sequences.