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A151754 Number of n-digit numbers that are divisible by 5^n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..30.

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

FORMULA

Lim n -> inf. a(n+1}/a{n) = 2.

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

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A151752.

Sequence in context: A153234 A293334 A266625 * A192065 A157672 A125899

Adjacent sequences: A151751 A151752 A151753 * A151755 A151756 A151757

KEYWORD

nonn,base

AUTHOR

Robert G. Wilson v, Jun 17 2009

STATUS

approved

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Last modified December 3 11:24 EST 2022. Contains 358517 sequences. (Running on oeis4.)