cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A152154 Positive residues of Pepin's Test for Fermat numbers using either 5 or 10 for the base.

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%I A152154 #6 Apr 03 2023 10:36:11
%S A152154 2,0,16,256,65536,3484838166,17225898269543404863,
%T A152154 6964187975677595099156927503004398881,
%U A152154 14553806122642016769237504145596730952769427034161327480375008633175279343120
%N A152154 Positive residues of Pepin's Test for Fermat numbers using either 5 or 10 for the base.
%C A152154 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 A152154 5 was the base originally used by Pepin. The base 10 gives the same results.
%C A152154 Any positive integer k for which the Jacobi symbol (k|F(n)) is -1 can be used as the base instead.
%D A152154 M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001, pp. 42-43.
%H A152154 Dennis Martin, <a href="/A152154/b152154.txt">Table of n, a(n) for n = 0..11</a>
%H A152154 Chris Caldwell, The Prime Pages: <a href="https://t5k.org/glossary/page.php?sort=PepinsTest">Pepin's Test</a>.
%F A152154 a(n) = 5^((F(n) - 1)/2) (mod F(n)), where F(n) is the n-th Fermat Number
%e A152154 a(4) = 5^(32768) (mod 65537) = 65536 = -1 (mod F(4)), therefore F(4) is prime.
%e A152154 a(5) = 5^(2147483648) (mod 4294967297) = 3484838166 (mod F(5)), therefore F(5) is composite.
%Y A152154 Cf. A000215, A019434, A152153, A152155, A152156.
%K A152154 nonn
%O A152154 0,1
%A A152154 Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 27 2008