A005937 Pseudoprimes to base 6. (Formerly M5246)

35, 185, 217, 301, 481, 1105, 1111, 1261, 1333, 1729, 2465, 2701, 2821, 3421, 3565, 3589, 3913, 4123, 4495, 5713, 6533, 6601, 8029, 8365, 8911, 9331, 9881, 10585, 10621, 11041, 11137, 12209, 14315, 14701, 15841, 16589, 17329, 18361, 18721

Offset

1,1

Comments

Theorem: If both numbers q and 2q-1 are primes and n=q*(2q-1) then 6^(n-1) == 1 (mod n) (n is in the sequence) iff q is of the form 12k+1. 2701, 18721, 49141, 104653, 226801, 665281, ... are such terms. This sequence is a subsequence of A122783. - Farideh Firoozbakht, Sep 12 2006

Composite numbers k such that 6^(k-1) == 1 (mod k). - Michel Lagneau, Feb 18 2012

References

R. K. Guy, Unsolved Problems in Number Theory, A12.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

R. J. Mathar, T. D. Noe, and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (Mathar 1..118, Noe 119..1000, Greathouse 1001..10000)

C. Pomerance & N. J. A. Sloane, Correspondence, 1991

Index entries for sequences related to pseudoprimes

Mathematica

Select[Range[20000], ! PrimeQ[ # ] && PowerMod[6, #-1, # ] == 1 &] (* Farideh Firoozbakht, Sep 12 2006 *)

Crossrefs

Cf. A001567 (pseudoprimes to base 2), A122783.

Sequence in context: A220047 A101954 A220201 * A341043 A219831 A184200

Adjacent sequences: A005934 A005935 A005936 * A005938 A005939 A005940

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Farideh Firoozbakht, Sep 12 2006

Status

approved