A025721 Index of 7^n within the sequence of the numbers of the form 3^i*7^j.

1, 3, 7, 13, 21, 30, 41, 54, 69, 85, 103, 123, 145, 169, 194, 221, 250, 281, 313, 347, 383, 421, 460, 501, 544, 589, 636, 684, 734, 786, 840, 895, 952, 1011, 1072, 1134, 1198, 1264, 1332, 1402, 1473, 1546, 1621, 1698, 1776, 1856, 1938, 2022, 2108, 2195, 2284

Offset

0,2

Comments

Positions of zeros in A025642. - R. J. Mathar, Jul 06 2025

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

From Amiram Eldar, Nov 13 2025: (Start)

A003594(a(n)) = 7^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_3(7) (A152565).

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

Example

a(0) = 1, a(1) = 3 and a(2) = 7 because the first 7 numbers of the form 3^i * 7^j with i >= 0 and j >= 0 are 1, 3, 7, 9, 21, 27 and 49. - Robert Israel, Aug 20 2024

Maple

dA:= map(t -> 1+ilog[3](7^t), [$0..100]):
ListTools:-PartialSums(dA); # Robert Israel, Aug 20 2024

Mathematica

Accumulate[Table[Ceiling[n * Log[3, 7]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Crossrefs

Cf. A000420, A003594, A025642, A152565.

Sequence in context: A299476 A077853 A256588 * A298267 A235532 A195020

Adjacent sequences: A025718 A025719 A025720 * A025722 A025723 A025724

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 13 2025

Status

approved