%I A152156
%S A152156 1,0,1,1,1,810129131,1220845804166146754,
%T A152156 6964187975677595099156927503004398881,
%U A152156 14553806122642016769237504145596730952769427034161327480375008633175279343120
%V A152156 -1,0,-1,-1,-1,-810129131,-1220845804166146754,
%W A152156 6964187975677595099156927503004398881,
%X A152156 14553806122642016769237504145596730952769427034161327480375008633175279343120
%N A152156 Minimal residues of Pepin's Test for Fermat Numbers using either 5 or 
               10 for the base.
%C A152156 For n=0 or n>=2 the Fermat Number F(n) is prime if and only if 5^((F(n) 
               - 1)/2) is congruent to -1 (mod F(n)).
%C A152156 5 was the base originally used by Pepin. The base 10 gives the same results.
%C A152156 Any positive integer k for which the Jacobi symbol (k|F(n)) is -1 can 
               be used as the base instead.
%D A152156 M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag 
               NY 2001, pp. 42-43.
%H A152156 Dennis Martin, <a href="b152156.txt">Table of n, a(n) for n = 0..11</
               a>
%H A152156 Chris Caldwell, The Prime Pages: <a href="http://primes.utm.edu/glossary/
               page.php?sort=PepinsTest">Pepin's Test</a>.
%H A152156 M. Krizek, F. Luca & L. Somer, <a href="http://books.google.com/books?id=6JCBqZ0CMqgC&pg=PA42&vq=pepin's+test\
               &dq=17+lectures+on+fermat+numbers&source=gbs_search_s&cad=0">17 Lectures 
               on Fermat Numbers, pp. 42-43</a>.
%F A152156 a(n) = 5^((F(n) - 1)/2) (mod F(n)), where F(n) is the n-th Fermat Number
%e A152156 a(4) = 5^(32768) (mod 65537) = 65536 = -1 (mod F(4)), therefore F(4) 
               is prime.
%e A152156 a(5) = 5^(2147483648) (mod 4294967297) = -810129131 (mod F(5)), therefore 
               F(5) is composite.
%Y A152156 Cf. A000215, A019434, A152153, A152154, A152155
%Y A152156 Sequence in context: A166227 A104829 A166072 this_sequence A017540 A132216 
               A091340
%Y A152156 Adjacent sequences: A152153 A152154 A152155 this_sequence A152157 A152158 
               A152159
%K A152156 sign
%O A152156 0,6
%A A152156 Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 27 2008