A054706 Number of powers of 5 modulo n.

1, 1, 2, 1, 2, 2, 6, 2, 6, 2, 5, 2, 4, 6, 3, 4, 16, 6, 9, 2, 6, 5, 22, 2, 3, 4, 18, 6, 14, 3, 3, 8, 10, 16, 7, 6, 36, 9, 4, 3, 20, 6, 42, 5, 7, 22, 46, 4, 42, 3, 16, 4, 52, 18, 6, 6, 18, 14, 29, 3, 30, 3, 6, 16, 5, 10, 22, 16, 22, 7, 5, 6, 72, 36, 4, 9, 30, 4, 39, 5, 54, 20, 82, 6, 17, 42, 14

Offset: 1

Author

Henry Bottomley, Apr 20 2000

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from David W. Wilson)

Crossrefs

Cf. A007736, A112765.

Cf. A054703 (base 2), A054704 (3), A054705 (4), A054707 (6), A054708 (7), A054709 (8), A054717 (9), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054715 (15), A054716 (16).

Programs

Mathematica

a[n_] := Module[{e = IntegerExponent[n, 5]}, e + MultiplicativeOrder[5, n/5^e]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

Formula

a(n) = A007736(n) + A112765(n). - Amiram Eldar, Aug 25 2024