A025738 Index of 9^n within the sequence of the numbers of the form 8^i*9^j.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 191, 212, 234, 257, 281, 306, 332, 359, 387, 416, 446, 477, 509, 542, 576, 611, 647, 684, 723, 763, 804, 846, 889, 933, 978, 1024, 1071, 1119, 1168, 1218, 1269, 1321, 1374, 1428, 1483, 1540, 1598

Offset

0,2

Comments

Positions of zeros in A025676. - 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)) = 9^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_8(9) (A154010).

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

Mathematica

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

Crossrefs

Cf. A001019, A025633, A025676, A154010.

Sequence in context: A176659 A109811 A025747 * A078256 A025731 A077367

Adjacent sequences: A025735 A025736 A025737 * A025739 A025740 A025741

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 14 2025

Status

approved