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A020145 Pseudoprimes to base 17. 2
4, 8, 9, 16, 45, 91, 145, 261, 781, 1111, 1228, 1305, 1729, 1885, 2149, 2821, 3991, 4005, 4033, 4187, 4912, 5365, 5662, 5833, 6601, 6697, 7171, 8481, 8911, 10585, 11476, 12403, 12673, 13333, 13833, 15805, 15841, 16705, 19345, 19729, 20591, 21781, 22791 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Composite numbers n such that 17^(n-1) == 1 (mod n).

According to Karsten Meyer, May 16 2006, the terms 4, 8, 9 and 16 should be excluded, following the strict definition in Crandall and Pomerance (p. 132) that even numbers and squares are not pseudoprimes regardless of congruence. [clarified by Alonso del Arte, Feb 17 2020]

REFERENCES

Richard Crandall and Carl 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 and T. D. Noe, Table of n, a(n) for n = 1..1000 (R. J. Mathar to 799 terms)

Fred Richman, Primality testing with Fermat's little theorem

Index entries for sequences related to pseudoprimes

EXAMPLE

17^3 = 4913 = 1 mod 4, so 4 is in the sequence (note the Crandall and Pomerance caveat, however).

17^4 = 83521 = 1 mod 5, but 5 is actually prime, so it's not in the sequence.

17^5 = 1419857 = 5 mod 6, so 6 is not in the sequence either.

MATHEMATICA

base = 17; pp17 = {}; n = 1; While[Length[pp17] < 100, n++; If[!PrimeQ[n] && PowerMod[base, n - 1, n] == 1, AppendTo[pp17, n]]]; pp17 (* T. D. Noe, Feb 21 2012 *)

Select[Range[23000], !PrimeQ[#] && PowerMod[17, # - 1, #] == 1 &] (* Harvey P. Dale, Apr 20 2019 *)

CROSSREFS

Cf. A001567 (pseudoprimes to base 2).

Sequence in context: A089042 A227243 A272575 * A202271 A334858 A162898

Adjacent sequences:  A020142 A020143 A020144 * A020146 A020147 A020148

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified September 24 21:35 EDT 2020. Contains 337322 sequences. (Running on oeis4.)