A025695 Index of 2^n within the sequence of the numbers of the form 2^i*10^j.

1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 23, 27, 31, 35, 40, 45, 50, 56, 62, 68, 75, 82, 89, 96, 104, 112, 120, 129, 138, 147, 157, 167, 177, 187, 198, 209, 220, 232, 244, 256, 269, 282, 295, 308, 322, 336, 350, 365, 380, 395, 411, 427, 443, 459, 476, 493, 510, 528, 546, 564, 583

Offset

0,2

Comments

Positions of zeros in A025684. - 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)

A025612(a(n)) = 2^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_10(2) (A007524).

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 13 2025 *)

Crossrefs

Cf. A000079, A007524, A025612, A025684.

Sequence in context: A024174 A008739 A280706 * A025694 A022796 A008748

Adjacent sequences: A025692 A025693 A025694 * A025696 A025697 A025698

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 13 2025

Status

approved