

A020138


Pseudoprimes to base 9.


8



4, 8, 28, 52, 91, 121, 205, 286, 364, 511, 532, 616, 671, 697, 703, 946, 949, 1036, 1105, 1288, 1387, 1541, 1729, 1891, 2465, 2501, 2665, 2701, 2806, 2821, 2926, 3052, 3281, 3367, 3751, 4376, 4636, 4961, 5356, 5551, 6364, 6601, 6643, 7081, 7381, 7913, 8401
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OFFSET

1,1


COMMENTS

This sequence is a subsequence of A122786. In fact the terms are composite terms n of A122786 such that gcd(n,3)=1. Theorem: If both numbers q & 2q1 are primes greater than 3 and n=q*(2q1) then 9^(n1)==1 (mod n) (n is in the sequence). So for n>2 A005382(n)* (2*A005382(n)1) is in the sequence; 91,703,1891,2701,12403,18721,... is the related subsequence.  Farideh Firoozbakht, Sep 15 2006
Composite numbers n such that 9^(n1) == 1 (mod n).


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..159 from R. J. Mathar, terms 160..1000 from T. D. Noe)
Index entries for sequences related to pseudoprimes


MATHEMATICA

Select[Range[8500], ! PrimeQ[ # ] && PowerMod[9, (#  1), # ] == 1 &] (* Farideh Firoozbakht, Sep 15 2006 *)


CROSSREFS

Cf. A001567 (pseudoprimes to base 2), A005382, A122786.
Sequence in context: A104042 A338429 A117864 * A306448 A090083 A034515
Adjacent sequences: A020135 A020136 A020137 * A020139 A020140 A020141


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



