A025700 Index of 3^n within the sequence of the numbers of the form 3^i * 10^j.

1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50, 57, 65, 73, 82, 91, 101, 111, 122, 133, 144, 156, 168, 181, 194, 208, 222, 237, 252, 268, 284, 301, 318, 336, 354, 373, 392, 412, 432, 453, 474, 495, 517, 539, 562, 585, 609, 633, 658, 683, 709, 735, 762, 789, 817, 845, 874

Offset

0,2

Comments

First term different from A033638 is a(24) = 144 != A033638(24) = 145.

Positions of zeros in A025685. - 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)

A025616(a(n)) = 3^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_10(3) (A114490).

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

Mathematica

Accumulate[Table[Ceiling[n * Log10[3]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Prog

(PARI) a(n) = vecsearch(setbinop((i, j)->3^i * 10^j, [0..n], [0..logint(10^n, 3)]), 3^n); \\ Michel Marcus, Jun 24 2023

Crossrefs

Cf. A000244, A011557, A025616, A025685, A033638, A114490.

Sequence in context: A022780 A075353 A132278 * A033638 A194205 A136413

Adjacent sequences: A025697 A025698 A025699 * A025701 A025702 A025703

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset 0 from Michel Marcus, Jun 24 2023

Status

approved