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A020141 Pseudoprimes to base 13. 2
4, 6, 12, 21, 85, 105, 231, 244, 276, 357, 427, 561, 1099, 1785, 1891, 2465, 2806, 3605, 5028, 5149, 5185, 5565, 6601, 7107, 8841, 8911, 9577, 9637, 10308, 10585, 11305, 12403, 12621, 13019, 13345, 13461, 13685, 14491, 14981, 15051, 15505, 15841, 17803 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

According to Karsten Meyer, May 16 2006, 4, 6 and 12 should be excluded, following the strict definition in Crandall and Pomerance.

Composite numbers n such that 13^(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)

LINKS

R. J. Mathar and T. D. Noe, Table of n, a(n) for n = 1..1000 (R. J. Mathar to 788 terms)

Index entries for sequences related to pseudoprimes

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

MATHEMATICA

base = 13; t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n] && PowerMod[base, n-1, n] == 1, AppendTo[t, n]]]; t (* T. D. Noe, Feb 21 2012 *)

CROSSREFS

Cf. A001567 (pseudoprimes to base 2).

Sequence in context: A110935 A128034 A027150 * A049478 A263458 A163776

Adjacent sequences:  A020138 A020139 A020140 * A020142 A020143 A020144

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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