A054710 Number of powers of 10 mod n.

1, 2, 1, 3, 2, 2, 6, 4, 1, 2, 2, 3, 6, 7, 2, 5, 16, 2, 18, 3, 6, 3, 22, 4, 3, 7, 3, 8, 28, 2, 15, 6, 2, 17, 7, 3, 3, 19, 6, 4, 5, 7, 21, 4, 2, 23, 46, 5, 42, 3, 16, 8, 13, 4, 3, 9, 18, 29, 58, 3, 60, 16, 6, 7, 7, 3, 33, 18, 22, 7, 35, 4, 8, 4, 3, 20, 6, 7, 13, 5, 9, 6, 41, 8, 17, 22, 28, 5, 44, 2

Offset: 1

Author

Henry Bottomley, Apr 20 2000

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A007732, A051628, A121341.

Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054717 (9), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054715 (15), A054716 (16).

Programs

Mathematica

Table[Length[Union[PowerMod[10, Range[0,n], n]]], {n,100}] (* T. D. Noe, Aug 30 2006 *)
a[n_] := Module[{e = IntegerExponent[n, {2, 5}]}, Max[e] + MultiplicativeOrder[10, n/Times @@ ({2, 5}^e)]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

Formula

a(n) = A007732(n) + A051628(n). - Amiram Eldar, Aug 25 2024