A025728 Index of 8^n within the sequence of the numbers of the form 3^i*8^j (A025615).

1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 110, 131, 154, 179, 206, 235, 266, 299, 334, 370, 408, 448, 490, 534, 580, 628, 678, 730, 783, 838, 895, 954, 1015, 1078, 1143, 1210, 1279, 1350, 1422, 1496, 1572, 1650, 1730, 1812, 1896, 1982, 2070, 2159, 2250, 2343, 2438

Offset

0,2

Comments

Positions of zeros in A025643. - R. J. Mathar, Jul 06 2025

Links

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

Formula

A025615(a(n)) = 8^n. - Bernard Schott, Dec 27 2021

From Amiram Eldar, Nov 13 2025: (Start)

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_3(8) (A113210).

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

Mathematica

Accumulate[Table[Ceiling[n * Log[3, 8]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Crossrefs

Cf. A001018, A025615, A025643, A025699 (similar for 3^n), A113210.

Sequence in context: A102508 A115298 A161206 * A084537 A002061 A247890

Adjacent sequences: A025725 A025726 A025727 * A025729 A025730 A025731

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 13 2025

Status

approved