A020147 Pseudoprimes to base 19.

6, 9, 15, 18, 45, 49, 153, 169, 343, 561, 637, 889, 905, 906, 1035, 1105, 1629, 1661, 1849, 1891, 2353, 2465, 2701, 2821, 2955, 3201, 4033, 4681, 5461, 5466, 5713, 6223, 6541, 6601, 6697, 7957, 8145, 8281, 8401, 8869, 9211, 9997, 10021, 10515, 10585

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

According to Karsten Meyer, May 16 2006, 6, 9 and 18 should be excluded, following the strict definition in Crandall and Pomerance.

Composite numbers n such that 19^(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, Table of n, a(n) for n = 1..1000
• F. Richman, Primality testing with Fermat's little theorem
• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A001567 (pseudoprimes to base 2).

Programs

Mathematica

base = 19; 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 *)