A020141 Pseudoprimes to base 13.

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

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