A122786 Nonprimes n such that 9^n == 9 (mod n).

1, 4, 6, 8, 9, 12, 15, 18, 24, 28, 36, 45, 52, 66, 72, 91, 121, 153, 205, 276, 286, 364, 366, 369, 396, 435, 511, 532, 561, 616, 671, 697, 703, 726, 804, 946, 949, 1035, 1036, 1105, 1128, 1288, 1387, 1541, 1729, 1737, 1845, 1854, 1891, 2196, 2465, 2501, 2556, 2665

Offset: 1

Author

Farideh Firoozbakht, Sep 12 2006

Keywords

• nonn

Comments

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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005382, A020138.

Programs

Maple

q:= n-> is(not isprime(n) and (9 &^ n mod n) = (9 mod n)):
select(q, [$1..3000])[];  # Alois P. Heinz, Mar 06 2019

Mathematica

Select[Range[4000], ! PrimeQ[ # ] && Mod[9^#, # ] == Mod[9, # ] &]
Join[{1,4,6,8,9},Select[Range[3000],CompositeQ[#]&&PowerMod[9,#,#]==9&]] (* Harvey P. Dale, Jul 17 2014 *)

PARI

isok(n) = !isprime(n) && (Mod(9,n)^n == Mod(9, n)); \\ Michel Marcus, Mar 06 2019