A025739 Index of 9^n within the sequence of the numbers of the form 9^i*10^j.

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 253, 275, 298, 322, 347, 373, 400, 428, 457, 487, 518, 550, 583, 617, 652, 688, 725, 763, 802, 842, 883, 925, 967, 1010, 1054, 1099, 1145, 1192, 1240, 1289, 1339, 1390, 1442

Offset

0,2

Comments

Positions of zeros in A025691. - 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)

A025635(a(n)) = 9^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_10(9) (A104139).

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

Mathematica

Accumulate[Table[Ceiling[n * Log10[9]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 14 2025 *)

Crossrefs

Cf. A001019, A025635, A025691, A104139.

Sequence in context: A254835 A025725 A025732 * A000124 A152947 A212369

Adjacent sequences: A025736 A025737 A025738 * A025740 A025741 A025742

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 14 2025

Status

approved