A025694 Index of 2^n within the sequence of the numbers of the form 2^i * 9^j.

1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 23, 27, 31, 36, 41, 46, 52, 58, 64, 70, 77, 84, 91, 99, 107, 115, 124, 133, 142, 152, 162, 172, 183, 194, 205, 217, 229, 241, 253, 266, 279, 292, 306, 320, 334, 349, 364, 379, 395, 411, 427, 444, 461, 478, 496, 514, 532, 550, 569, 588, 607

Offset

0,2

Comments

Positions of zeros in A025678. - 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)

A025611(a(n)) = 2^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_9(2) (A152747).

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

Maple

f:= proc(n) local j, s, t;
      t:= n;
      for j from 1 do
         s:= ilog2(9^j);
         if s >= n then return t fi;
         t:= t + n-1-s;
      od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 09 2016

Mathematica

Accumulate[Table[Ceiling[n * Log[9, 2]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Prog

(PARI) a(n)=my(N=1); n+1+sum(i=1, n, logint(N<<=1, 9)); \\ Charles R Greathouse IV, Jan 11 2018
(PARI) first(n)=my(s, N=1/2); vector(n+1, i, s+=logint(N<<=1, 9)+1) \\ Charles R Greathouse IV, Jan 11 2018

Crossrefs

Cf. A000079, A025611, A025678, A152747.

Sequence in context: A008739 A280706 A025695 * A022796 A008748 A089649

Adjacent sequences: A025691 A025692 A025693 * A025695 A025696 A025697

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Charles R Greathouse IV, Jan 11 2018

Status

approved