A151754 Number of n-digit numbers that are divisible by 5^n.

1, 3, 7, 14, 28, 57, 115, 230, 460, 921, 1843, 3686, 7372, 14745, 29491, 58982, 117964, 235929, 471859, 943718, 1887436, 3774873, 7549747, 15099494, 30198988, 60397977, 120795955, 241591910, 483183820, 966367641, 1932735283, 3865470566, 7730941132, 15461882265

Offset: 1

Author

Robert G. Wilson v, Jun 17 2009

Keywords

• nonn
• base
• easy

Examples

			a(1)=1 because 5 divides only 5,
a(2)=3 because 25 divides {25, 50 & 75},
a(3)=7 because 125 divides {125, 250, 375, 500, 625, 750 & 925}, etc.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-2).

Crossrefs

Cf. A151752.

Programs

Mathematica

f[n_] := Floor[(10^n - 1)/5^n] - Floor[10^(n - 1)/5^n]; Array[f, 35]
LinearRecurrence[{3,-3,3,-2},{1,3,7,14},30] (* Harvey P. Dale, Feb 20 2016 *)

Formula

Limit_{n -> oo} a(n+1)/a(n) = 2.

a(n) = [(9/10)*2^n]. - David W. Wilson, Jun 18 2009

G.f.: x * ( 1+x^2-x^3 ) / ( (x-1)*(2*x-1)*(x^2+1) ). - R. J. Mathar, Feb 20 2011