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A020138 Pseudoprimes to base 9. 5
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 (list; graph; refs; listen; history; text; internal format)
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 & 2q-1 are primes greater than 3 and n=q*(2q-1) then 9^(n-1)==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^(n-1) == 1 (mod n).

LINKS

R. J. Mathar and T. D. Noe, Table of n, a(n) for n = 1..1000 (R. J. Mathar to 159 terms)

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: A099513 A104042 A117864 * A090083 A034515 A189546

Adjacent sequences:  A020135 A020136 A020137 * A020139 A020140 A020141

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.