A025718 Index of 6^n within the sequence of the numbers of the form 6^i*9^j.

1, 2, 4, 7, 11, 16, 21, 27, 34, 42, 51, 60, 70, 81, 93, 106, 120, 134, 149, 165, 182, 200, 218, 237, 257, 278, 300, 323, 346, 370, 395, 421, 448, 475, 503, 532, 562, 593, 624, 656, 689, 723, 758, 794, 830, 867, 905, 944, 984, 1024, 1065, 1107, 1150, 1194, 1239, 1284

Offset

0,2

Comments

Positions of zeros in A025680. - 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)

A025628(a(n)) = 6^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_9(6) (A153495).

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

Maple

with(priqueue):
initialize(PQ):
insert([-1, 0, 0], PQ):
count:= 0: R:= NULL:
for i from 1 while count < 100 do
  v:= extract(PQ);
if v[3] = 0 then R:= R, i; count:= count+1; insert([v[1]*6, v[2]+1, 0], PQ);
insert([v[1]*9, v[2], v[3]+1], PQ)
od:
R; # Robert Israel, Jan 21 2024

Mathematica

Accumulate[Table[Ceiling[n * Log[9, 6]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Crossrefs

Cf. A000400, A025628, A025680, A153495.

Sequence in context: A067744 A307601 A194215 * A022783 A025708 A024673

Adjacent sequences: A025715 A025716 A025717 * A025719 A025720 A025721

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 13 2025

Status

approved