A025696 Index of 3^n within the sequence of the numbers of the form 3^i*4^j.

1, 2, 4, 7, 11, 15, 20, 26, 33, 41, 49, 58, 68, 79, 91, 103, 116, 130, 145, 161, 177, 194, 212, 231, 251, 271, 292, 314, 337, 360, 384, 409, 435, 462, 489, 517, 546, 576, 607, 638, 670, 703, 737, 772, 807, 843, 880, 918, 957, 996, 1036, 1077, 1119, 1162, 1205, 1249

Offset

0,2

Comments

Positions of zeros in A025645. - 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)

A025613(a(n)) = 3^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_4(3) (A094148).

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

Mathematica

Accumulate[Table[Ceiling[n * Log[4, 3]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Crossrefs

Cf. A000244, A025613, A025645, A094148.

Sequence in context: A025709 A036700 A025719 * A077169 A094277 A263995

Adjacent sequences: A025693 A025694 A025695 * A025697 A025698 A025699

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 13 2025

Status

approved