A020139 Pseudoprimes to base 11.

10, 15, 70, 133, 190, 259, 305, 481, 645, 703, 793, 1105, 1330, 1729, 2047, 2257, 2465, 2821, 4577, 4921, 5041, 5185, 6601, 7869, 8113, 8170, 8695, 8911, 9730, 10585, 12403, 13333, 14521, 14981, 15841, 16705, 17711, 18705, 23377, 24130, 24727, 26335, 26467

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

According to Karsten Meyer, May 16 2006, 10 should be excluded, following the strict definition in Crandall and Pomerance.

Composite numbers n such that 11^(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)
• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 190, p. 57, Ellipses, Paris 2008.

Links

• R. J. Mathar and T. D. Noe, Table of n, a(n) for n = 1..1000 (R. J. Mathar to 726 terms)
• 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 = 11; 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 *)