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

Author

David W. Wilson

Keywords

• nonn

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

Crossrefs

Cf. A001567 (pseudoprimes to base 2).

Programs

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 *)