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Pseudoprimes to base 11.
4

%I #23 Aug 22 2017 09:36:12

%S 10,15,70,133,190,259,305,481,645,703,793,1105,1330,1729,2047,2257,

%T 2465,2821,4577,4921,5041,5185,6601,7869,8113,8170,8695,8911,9730,

%U 10585,12403,13333,14521,14981,15841,16705,17711,18705,23377,24130,24727,26335,26467

%N Pseudoprimes to base 11.

%C According to _Karsten Meyer_, May 16 2006, 10 should be excluded, following the strict definition in Crandall and Pomerance.

%C Composite numbers n such that 11^(n-1) == 1 (mod n).

%D 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)

%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 190, p. 57, Ellipses, Paris 2008.

%H R. J. Mathar and T. D. Noe, <a href="/A020139/b020139.txt">Table of n, a(n) for n = 1..1000</a> (R. J. Mathar to 726 terms)

%H F. Richman, <a href="http://math.fau.edu/Richman/carm.htm">Primality testing with Fermat's little theorem</a>

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%t 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 *)

%Y Cf. A001567 (pseudoprimes to base 2).

%K nonn

%O 1,1

%A _David W. Wilson_