A020138 Pseudoprimes to base 9.

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

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

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