A025705 - OEIS

%I #14 Nov 13 2025 02:23:28

%S 1,2,4,6,9,13,17,22,27,33,40,47,55,63,72,82,92,103,114,126,139,152,

%T 166,180,195,211,227,244,261,279,298,317,337,357,378,400,422,445,468,

%U 492,517,542,568,594,621,649,677,706,735,765,796,827,859,891,924,958,992,1027

%N Index of 4^n within the sequence of the numbers of the form 4^i*10^j.

%C Positions of zeros in A025686. - _R. J. Mathar_, Jul 06 2025

%H Amiram Eldar, <a href="/A025705/b025705.txt">Table of n, a(n) for n = 0..10000</a>

%F From _Amiram Eldar_, Nov 13 2025: (Start)

%F A025621(a(n)) = 4^n.

%F a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_10(4) (A114493).

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

%t Accumulate[Table[Ceiling[n * Log10[4]], {n, 0, 60}]] + 1 (* _Amiram Eldar_, Nov 13 2025 *)

%Y Cf. A000302, A025621, A025686, A114493.

%K nonn,easy

%O 0,2

%A _David W. Wilson_

%E Offset corrected by _Amiram Eldar_, Nov 13 2025