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A005938 Pseudoprimes to base 7.
(Formerly M4168)
16
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

According to Karsten Meyer, 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, Sep 14 2006

Composite numbers n such that 7^(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)

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, T. D. Noe and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..87448 (terms a(1)-a(697) from R. J. Mathar, a(698)-a(1000) from T. D. Noe)

J. Bernheiden, Pseudoprimes (Text in German)

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

Index entries for sequences related to pseudoprimes

MATHEMATICA

Select[Range[31000], ! PrimeQ[ # ] && PowerMod[7, (# - 1), # ] == 1 &] (* Farideh Firoozbakht, Sep 14 2006 *)

CROSSREFS

Pseudoprimes to other bases: A001567 (2), A005935 (3), A005936 (5), A005937 (6), A005939 (10).

Cf. A005382, A122784.

Sequence in context: A199008 A090566 A041064 * A157025 A174401 A036175

Adjacent sequences:  A005935 A005936 A005937 * A005939 A005940 A005941

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.