A025703 Index of 4^n within the sequence of the numbers of the form 4^i*6^j.

1, 2, 4, 7, 11, 15, 20, 26, 33, 40, 48, 57, 67, 78, 89, 101, 114, 128, 142, 157, 173, 190, 208, 226, 245, 265, 286, 307, 329, 352, 376, 400, 425, 451, 478, 506, 534, 563, 593, 624, 655, 687, 720, 754, 789, 824, 860, 897, 935, 973, 1012, 1052, 1093, 1135, 1177, 1220

Offset

0,2

Comments

First differs from A025709 at a(84).

Positions of zeros in A025658. - R. J. Mathar, Jul 06 2025

Links

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

Formula

a(n) = n + 1 + Sum_{j = 1 .. n} floor(j*log_6(4)). - Robert Israel, May 10 2015

From Amiram Eldar, Nov 13 2025: (Start)

A025618(a(n)) = 4^n.

a(n) ~ c * n^2 / 2, where c = log_6(4) (A153102). (End)

Maple

N:= 200: # to get a(0) to a(N)
[$1..N+1] + ListTools:-PartialSums([seq(floor(j*log[6](4)), j=0..N)]); # Robert Israel, May 10 2015

Mathematica

Accumulate[Table[Ceiling[n * Log[6, 4]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Prog

(PARI) a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=4, 6)); \\ Charles R Greathouse IV, Jan 11 2018
(PARI) first(n)=my(s, N=1/4); vector(n+1, i, s+=logint(N*=4, 6)+1) \\ Charles R Greathouse IV, Jan 11 2018

Crossrefs

Cf. A000302, A025618, A025658, A025709, A153102.

Sequence in context: A078617 A199085 A247184 * A025709 A036700 A025719

Adjacent sequences: A025700 A025701 A025702 * A025704 A025705 A025706

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Edited and offset corrected by Robert Israel, May 10 2015

Status

approved