A025729 Index of 8^n within the sequence of the numbers of the form 5^i*8^j.

1, 3, 6, 10, 16, 23, 31, 41, 52, 64, 77, 92, 108, 125, 144, 164, 185, 207, 231, 256, 282, 310, 339, 369, 401, 434, 468, 503, 540, 578, 617, 658, 700, 743, 787, 833, 880, 928, 978, 1029, 1081, 1134, 1189, 1245, 1302, 1361, 1421, 1482, 1545, 1609, 1674, 1740, 1808

Offset

0,2

Comments

Positions of zeros in A025653. - R. J. Mathar, Jul 06 2025

Links

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

Formula

From Amiram Eldar, Nov 13 2025: (Start)

A025623(a(n)) = 8^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_5(8) (A153739).

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

Mathematica

Accumulate[Table[Ceiling[n * Log[5, 8]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Crossrefs

Cf. A001018, A025623, A025653, A153739.

Differs from A025714 at a(65).

Sequence in context: A025744 A180746 A025714 * A011913 A024531 A034198

Adjacent sequences: A025726 A025727 A025728 * A025730 A025731 A025732

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 13 2025

Status

approved