A025692 Index of 2^n within the sequence of the numbers of the form 2^i*6^j.

1, 2, 3, 5, 7, 9, 12, 15, 19, 23, 27, 32, 37, 43, 49, 55, 62, 69, 76, 84, 92, 101, 110, 119, 129, 139, 150, 161, 172, 184, 196, 208, 221, 234, 248, 262, 276, 291, 306, 322, 338, 354, 371, 388, 406, 424, 442, 461, 480, 499, 519, 539, 560, 581, 602, 624, 646, 669, 692, 715

Offset

0,2

Comments

Positions of zeros in A025656. - R. J. Mathar, Jul 06 2025

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000 (terms 0..2500 from Robert Israel)

Formula

From Amiram Eldar, Nov 13 2025: (Start)

A025610(a(n)) = 2^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_6(2) (A152683).

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

Maple

N:= 100: # for a(0)..a(N)
S:= sort([seq(seq(2^i*6^j, i=0..ilog2(2^N/6^j)), j=0..floor(log[6](2^N)))]):
seq(ListTools:-BinarySearch(S, 2^i), i=0..N); # Robert Israel, Jan 12 2021

Mathematica

Accumulate[Table[Ceiling[n * Log[6, 2]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Crossrefs

Cf. A000079, A025610, A025656, A152683.

Sequence in context: A005704 A022782 A283968 * A137285 A062441 A059290

Adjacent sequences: A025689 A025690 A025691 * A025693 A025694 A025695

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Robert Israel, Jan 12 2021

Status

approved