A025705 Index of 4^n within the sequence of the numbers of the form 4^i*10^j.

1, 2, 4, 6, 9, 13, 17, 22, 27, 33, 40, 47, 55, 63, 72, 82, 92, 103, 114, 126, 139, 152, 166, 180, 195, 211, 227, 244, 261, 279, 298, 317, 337, 357, 378, 400, 422, 445, 468, 492, 517, 542, 568, 594, 621, 649, 677, 706, 735, 765, 796, 827, 859, 891, 924, 958, 992, 1027

Offset

0,2

Comments

Positions of zeros in A025686. - 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)

A025621(a(n)) = 4^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_10(4) (A114493).

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

Mathematica

Accumulate[Table[Ceiling[n * Log10[4]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Crossrefs

Cf. A000302, A025621, A025686, A114493.

Sequence in context: A194209 A183143 A184977 * A022792 A025697 A255977

Adjacent sequences: A025702 A025703 A025704 * A025706 A025707 A025708

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 13 2025

Status

approved