This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A152153 Positive residues of Pepin's Test for Fermat numbers using the base 3. 4
 0, 4, 16, 256, 65536, 10324303, 11860219800640380469, 110780954395540516579111562860048860420, 5864545399742183862578018016183410025465491904722516203269973267547486512819 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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)). REFERENCES M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001, pp. 42-43. LINKS Dennis Martin, Table of n, a(n) for n = 0..11 Chris Caldwell, The Prime Pages: Pepin's Test. FORMULA a(n) = 3^((F(n) - 1)/2) (mod F(n)), where F(n) is the n-th Fermat Number EXAMPLE a(4) = 3^(32768) (mod 65537) = 65536 = -1 (mod F(4)), therefore F(4) is prime. a(5) = 3^(2147483648) (mod 4294967297) = 10324303 (mod F(5)), therefore F(5) is composite. CROSSREFS Cf. A000215, A019434, A152154, A152155, A152156. Sequence in context: A152921 A215116 A212297 * A144988 A067172 A013089 Adjacent sequences:  A152150 A152151 A152152 * A152154 A152155 A152156 KEYWORD nonn AUTHOR Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 27 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 19 16:36 EDT 2019. Contains 323395 sequences. (Running on oeis4.)