

A005937


Pseudoprimes to base 6.
(Formerly M5246)


11



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
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OFFSET

1,1


COMMENTS

Theorem: If both numbers q and 2q1 are primes and n=q*(2q1) then 6^(n1)==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 n such that 6^(n1) == 1 (mod n).  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 (Mather 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 * A219831 A184200 A219942
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



