A054709 Number of powers of 8 modulo n.

1, 2, 2, 2, 4, 3, 1, 2, 2, 5, 10, 3, 4, 2, 4, 3, 8, 3, 6, 5, 2, 11, 11, 3, 20, 5, 6, 2, 28, 5, 5, 3, 10, 9, 4, 3, 12, 7, 4, 5, 20, 3, 14, 11, 4, 12, 23, 4, 7, 21, 8, 5, 52, 7, 20, 2, 6, 29, 58, 5, 20, 6, 2, 3, 4, 11, 22, 9, 22, 5, 35, 3, 3, 13, 20, 7, 10, 5, 13, 6, 18, 21, 82, 3, 8, 15, 28

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 David W. Wilson)

Crossrefs

Cf. A007739.

Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054717 (9), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054715 (15), A054716 (16).

Programs

Mathematica

a[n_] := IntegerExponent[4*n, 8] + MultiplicativeOrder[8, n/2^IntegerExponent[n, 2]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

Formula

a(n) = valuation(4*n, 8) + A007739(n). - Amiram Eldar, Aug 25 2024