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Search: id:A005938
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| A005938 |
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Pseudoprimes to base 7.
(Formerly M4168)
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+0
4
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| 6, 25, 325, 561, 703, 817, 1105, 1825, 2101, 2353, 2465, 3277, 4525, 4825, 6697, 8321, 10225, 10585, 10621, 11041, 11521, 12025, 13665, 14089, 16725, 16806, 18721, 19345, 20197, 20417, 20425, 22945, 25829, 26419, 29234, 29341, 29857, 29891, 30025, 30811
(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, 6 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) and n=q*(2q-1) then 7^(n-1)==1 (mod 7)(n is in the sequence) iff q=2 or mod(q,14) is in the set {1, 5, 13}. 6,703,18721,38503,88831,104653,146611,188191,... are such terms. This sequence is a subsequence of A122784. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 14 2006
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REFERENCES
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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)
R. K. Guy, Unsolved Problems in Number Theory, A12.
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LINKS
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R. J. Mathar, Table of n, a(n) for n=1..129
J. Bernheiden, Pseudoprimes (Text in German)
F. Richman, Primality testing with Fermat's little theorem
Index entries for sequences related to pseudoprimes
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MATHEMATICA
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Select[Range[31000], ! PrimeQ[ # ] && PowerMod[7, (# - 1), # ] == 1 &] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 14 2006
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CROSSREFS
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Cf. A005382, A122784.
Adjacent sequences: A005935 A005936 A005937 this_sequence A005939 A005940 A005941
Sequence in context: A042529 A090566 A041064 this_sequence A036175 A154869 A043354
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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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