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A005936 Pseudoprimes to base 5.
(Formerly M3712)
10
4, 124, 217, 561, 781, 1541, 1729, 1891, 2821, 4123, 5461, 5611, 5662, 5731, 6601, 7449, 7813, 8029, 8911, 9881, 11041, 11476, 12801, 13021, 13333, 13981, 14981, 15751, 15841, 16297, 17767, 21361, 22791, 23653, 24211, 25327, 25351, 29341, 29539 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

According to Karsten Meyer, 4 should be excluded, following the strict definition in Crandall and Pomerance. - May 16 2006

Theorem: If both numbers q and (2q - 1) are primes (q is in the sequence A005382) then n = q*(2q - 1) is a pseudoprime to base 5 (n is in the sequence) if and only if q is of the form 10k + 1. 1891, 88831, 146611, 218791, 721801, ... are such terms. This sequence is a subsequence of A122782. - Farideh Firoozbakht, Sep 14 2006

Composite numbers n such that 5^(n-1) == 1 (mod n).

REFERENCES

R. Crandall and C. Pomerance, "Prime Numbers - A Computational Perspective", Second Edition, Springer Verlag 2005, ISBN 0-387-25282-7 Page 132 (Theorem 3.4.2. and Algorithm 3.4.3)

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 124, p. 43, Ellipses, Paris 2008.

R. K. Guy, Unsolved Problems in Number Theory, A12.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

R. J. Mathar and T. D. Noe, Table of n, a(n) for n = 1..1000 (R. J. Mathar to 776 terms)

J. Bernheiden, Pseudoprimes (Text in German)

F. Richman, Primality testing with Fermat's little theorem

Eric Weisstein's World of Mathematics, Fermat Pseudoprime

Index entries for sequences related to pseudoprimes

MATHEMATICA

base = 5; t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n] && PowerMod[base, n-1, n] == 1, AppendTo[t, n]]]; t (* T. D. Noe, Feb 21 2012 *)

CROSSREFS

Cf. A001567 (pseudoprimes to base 2), A005382, A122782.

Sequence in context: A064681 A219871 A232592 * A241648 A197779 A197610

Adjacent sequences:  A005933 A005934 A005935 * A005937 A005938 A005939

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from David W. Wilson Aug 15 1996.

STATUS

approved

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Last modified September 1 19:46 EDT 2014. Contains 246317 sequences.