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A020147 Pseudoprimes to base 19. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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 *)

CROSSREFS

Cf. A001567 (pseudoprimes to base 2).

Sequence in context: A316028 A316029 A316030 * A316031 A316032 A316033

Adjacent sequences:  A020144 A020145 A020146 * A020148 A020149 A020150

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified June 25 06:10 EDT 2019. Contains 324347 sequences. (Running on oeis4.)