A025740 Index of 10^n within the sequence of the numbers of the form 2^i*10^j.

1, 5, 12, 22, 36, 53, 73, 97, 124, 154, 188, 225, 265, 309, 356, 406, 460, 517, 577, 641, 708, 778, 852, 929, 1009, 1093, 1180, 1270, 1364, 1461, 1561, 1664, 1771, 1881, 1994, 2111, 2231, 2354, 2481, 2611, 2744, 2881, 3021, 3164, 3311, 3461, 3614, 3771, 3931

Offset

0,2

Comments

Positions of zeros in A025639. - 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)

A025612(a(n)) = 10^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_2(10) (A020862).

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

Mathematica

Accumulate[Table[Ceiling[n / Log10[2]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 14 2025 *)

Crossrefs

Partial sums of A123384.

Cf. A011557, A020862, A025612, A025639.

Sequence in context: A153818 A069627 A034971 * A225247 A299257 A298791

Adjacent sequences: A025737 A025738 A025739 * A025741 A025742 A025743

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 14 2025

Status

approved