A020147 - OEIS

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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

(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 A360395

Adjacent sequences: A020144 A020145 A020146 * A020148 A020149 A020150

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved