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
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
KEYWORD
nonn
AUTHOR
STATUS
approved