A025701 Index of 4^n within the sequence of the numbers of the form 3^i*4^j.

1, 3, 6, 10, 16, 23, 31, 40, 51, 63, 76, 90, 106, 123, 141, 160, 181, 203, 226, 250, 276, 303, 331, 361, 392, 424, 457, 492, 528, 565, 603, 643, 684, 726, 769, 814, 860, 907, 955, 1005, 1056, 1108, 1161, 1216, 1272, 1329, 1388, 1448, 1509, 1571, 1635, 1700, 1766

Offset

0,2

Comments

Positions of zeros in A025640. - 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)) = 4^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_3(4) (A100831).

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

Mathematica

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

Crossrefs

Cf. A000302, A025613, A025640, A100831.

Sequence in context: A293407 A194144 A330133 * A025744 A180746 A025714

Adjacent sequences: A025698 A025699 A025700 * A025702 A025703 A025704

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 13 2025

Status

approved