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%I #25 Mar 12 2020 20:32:48
%S 1,4,6,8,9,12,15,18,24,28,36,45,52,66,72,91,121,153,205,276,286,364,
%T 366,369,396,435,511,532,561,616,671,697,703,726,804,946,949,1035,
%U 1036,1105,1128,1288,1387,1541,1729,1737,1845,1854,1891,2196,2465,2501,2556,2665
%N Nonprimes n such that 9^n == 9 (mod n).
%C Theorem: If both numbers q and 2q-1 are primes and n=q*(2q-1) then 9^n==9 (mod n) (n is in the sequence). So A005382*(2*A005382-1)= 6,15,91,703,1891,2701,12403,18721,... is the related subsequence. A020138 is a subsequence of this sequence.
%H Alois P. Heinz, <a href="/A122786/b122786.txt">Table of n, a(n) for n = 1..10000</a>
%p q:= n-> is(not isprime(n) and (9 &^ n mod n) = (9 mod n)):
%p select(q, [$1..3000])[]; # _Alois P. Heinz_, Mar 06 2019
%t Select[Range[4000], ! PrimeQ[ # ] && Mod[9^#, # ] == Mod[9, # ] &]
%t Join[{1,4,6,8,9},Select[Range[3000],CompositeQ[#]&&PowerMod[9,#,#]==9&]] (* _Harvey P. Dale_, Jul 17 2014 *)
%o (PARI) isok(n) = !isprime(n) && (Mod(9,n)^n == Mod(9, n)); \\ _Michel Marcus_, Mar 06 2019
%Y Cf. A005382, A020138.
%K nonn
%O 1,2
%A _Farideh Firoozbakht_, Sep 12 2006
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