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.

A152153 Positive residues of Pepin's Test for Fermat numbers using the base 3.

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%I A152153 #6 Apr 03 2023 10:36:11
%S A152153 0,4,16,256,65536,10324303,11860219800640380469,
%T A152153 110780954395540516579111562860048860420,
%U A152153 5864545399742183862578018016183410025465491904722516203269973267547486512819
%N A152153 Positive residues of Pepin's Test for Fermat numbers using the base 3.
%C A152153 For n>=1 the Fermat Number F(n) is prime if and only if 3^((F(n) - 1)/2) is congruent to -1 (mod F(n)).
%D A152153 M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001, pp. 42-43.
%H A152153 Dennis Martin, <a href="/A152153/b152153.txt">Table of n, a(n) for n = 0..11</a>
%H A152153 Chris Caldwell, The Prime Pages: <a href="https://t5k.org/glossary/page.php?sort=PepinsTest">Pepin's Test</a>.
%F A152153 a(n) = 3^((F(n) - 1)/2) (mod F(n)), where F(n) is the n-th Fermat Number
%e A152153 a(4) = 3^(32768) (mod 65537) = 65536 = -1 (mod F(4)), therefore F(4) is prime.
%e A152153 a(5) = 3^(2147483648) (mod 4294967297) = 10324303 (mod F(5)), therefore F(5) is composite.
%Y A152153 Cf. A000215, A019434, A152154, A152155, A152156.
%K A152153 nonn
%O A152153 0,2
%A A152153 Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 27 2008