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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. J. Mathar, Table of n, a(n) for n=1..697
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.
Sequence in context: A042529 A090566 A041064 this_sequence A157025 A036175 A154869
Adjacent sequences: A005935 A005936 A005937 this_sequence A005939 A005940 A005941
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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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