

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




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



