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.
%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