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A054717
Number of powers of 9 modulo n.
16
1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 5, 2, 3, 3, 3, 2, 8, 2, 9, 2, 4, 5, 11, 2, 10, 3, 3, 3, 14, 3, 15, 4, 6, 8, 6, 2, 9, 9, 4, 2, 4, 4, 21, 5, 3, 11, 23, 3, 21, 10, 9, 3, 26, 3, 10, 3, 10, 14, 29, 3, 5, 15, 4, 8, 6, 6, 11, 8, 12, 6, 35, 2, 6, 9, 11, 9, 15, 4, 39, 2, 3, 4, 41, 4, 8, 21, 15, 5, 44, 3, 3
OFFSET
1,3
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from David W. Wilson)
FORMULA
a(n) = valuation(3*n, 9) + A007740(n). - Amiram Eldar, Aug 25 2024
EXAMPLE
Take the sequence 1, 9, 81, 729, ... and reduce mod n; count distinct terms. For n = 5 we get 1, 4, 1, 4, ... so a(5) = 2.
MATHEMATICA
With[{p9=9^Range[0, 50]}, Table[Length[Union[Mod[#, n]&/@p9]], {n, 100}]] (* Harvey P. Dale, Apr 22 2012 *)
a[n_] := IntegerExponent[3*n, 9] + MultiplicativeOrder[9, n/3^IntegerExponent[n, 3]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)
CROSSREFS
Cf. A007740.
Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054715 (15), A054716 (16).
Sequence in context: A333939 A272759 A272760 * A086421 A290399 A109400
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Apr 20 2000
STATUS
approved