|
Search: id:A005936
|
|
|
| A005936 |
|
Pseudoprimes to base 5.
(Formerly M3712)
|
|
+0
4
|
|
| 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)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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
|
|
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, Table of n, a(n) for n=1..776
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
|
|
CROSSREFS
|
Cf. A005382, A122782.
Sequence in context: A080179 A144993 A064681 this_sequence A090082 A068891 A073351
Adjacent sequences: A005933 A005934 A005935 this_sequence A005937 A005938 A005939
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from David W. Wilson Aug 15 1996.
|
|
|
Search completed in 0.002 seconds
|
