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A122786 Nonprimes n such that 9^n == 9 (mod n). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..54.

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 *)

PROG

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

CROSSREFS

Cf. A005382, A020138.

Sequence in context: A304242 A067012 A157942 * A092630 A079142 A062002

Adjacent sequences:  A122783 A122784 A122785 * A122787 A122788 A122789

KEYWORD

nonn

AUTHOR

Farideh Firoozbakht, Sep 12 2006

STATUS

approved

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Last modified May 22 14:32 EDT 2019. Contains 323480 sequences. (Running on oeis4.)