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%I #23 Jul 25 2021 02:39:34
%S 4,8,28,52,91,121,205,286,364,511,532,616,671,697,703,946,949,1036,
%T 1105,1288,1387,1541,1729,1891,2465,2501,2665,2701,2806,2821,2926,
%U 3052,3281,3367,3751,4376,4636,4961,5356,5551,6364,6601,6643,7081,7381,7913,8401
%N Pseudoprimes to base 9.
%C 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
%C Composite numbers n such that 9^(n-1) == 1 (mod n).
%H Amiram Eldar, <a href="/A020138/b020138.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..159 from R. J. Mathar, terms 160..1000 from T. D. Noe)
%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%t Select[Range[8500], ! PrimeQ[ # ] && PowerMod[9, (# - 1), # ] == 1 &] (* _Farideh Firoozbakht_, Sep 15 2006 *)
%Y Cf. A001567 (pseudoprimes to base 2), A005382, A122786.
%K nonn
%O 1,1
%A _David W. Wilson_
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