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Search: id:A005936
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| A005936 |
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Pseudoprimes to base 5.
(Formerly M3712)
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+0
4
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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According to Karsten Meyer (arbol01(AT)gmx.de), May 16 2006, 4 should be excluded, following the strict definition in Crandall and Pomerance.
Theorem: If both numbers q & (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) iff q is of the form 10k+1. 1891,88831,146611,218791,721801,... are such terms. This sequence is a subsequence of A122782. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 14 2006
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, A12.
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.
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LINKS
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R. J. Mathar, Table of n, a(n) for n=1..85
F. Richman, Primality testing with Fermat's little theorem
Eric Weisstein's World of Mathematics, Fermat Pseudoprime
Index entries for sequences related to pseudoprimes
J. Bernheiden, Pseudoprimes (Text in German)
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CROSSREFS
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Cf. A005382, A122782.
Adjacent sequences: A005933 A005934 A005935 this_sequence A005937 A005938 A005939
Sequence in context: A080179 A144993 A064681 this_sequence A090082 A068891 A073351
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from David W. Wilson Aug 15 1996.
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