A025732 Index of 8^n within the sequence of the numbers of the form 8^i*9^j.

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 190, 209, 229, 250, 272, 295, 319, 344, 370, 397, 425, 454, 484, 515, 547, 580, 614, 649, 685, 721, 758, 796, 835, 875, 916, 958, 1001, 1045, 1090, 1136, 1183, 1231, 1280, 1330, 1381, 1433

Offset

0,2

Comments

Positions of zeros in A025682. - R. J. Mathar, Jul 06 2025

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

From Amiram Eldar, Nov 14 2025: (Start)

A025633(a(n)) = 8^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_9(8) (A153756).

a(n) ~ c * n^2 / 2, where c is defined above. (End)

Mathematica

Accumulate[Table[Ceiling[n * Log[9, 8]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 14 2025 *)

Crossrefs

Cf. A001018, A025633, A025682, A153756.

Sequence in context: A025716 A254835 A025725 * A025739 A000124 A152947

Adjacent sequences: A025729 A025730 A025731 * A025733 A025734 A025735

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 14 2025

Status

approved