A130901 a(n) = Sum_{k=1..9} floor(10^n / k).

1, 26, 281, 2827, 28288, 282895, 2828967, 28289681, 282896824, 2828968252, 28289682538, 282896825395, 2828968253967, 28289682539681, 282896825396824, 2828968253968252, 28289682539682538, 282896825396825395, 2828968253968253967, 28289682539682539681

Offset

0,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (11,-10,-1,11,-10).

Formula

A055642(a(n)) = n.

From Chai Wah Wu, Jan 14 2021: (Start)

a(n) = 11*a(n-1) - 10*a(n-2) - a(n-3) + 11*a(n-4) - 10*a(n-5) for n > 7.

G.f.: (-5*x^7 - 2*x^6 + 2*x^5 + 16*x^4 - 3*x^3 + 5*x^2 + 15*x + 1)/((x - 1)*(x + 1)*(10*x - 1)*(x^2 - x + 1)). (End)

Example

a(1) = [10/1]+[10/2]+[10/3]+[10/4]+[10/5]+[10/6]+[10/7]+[10/8]+[10/9] = 10 + 5 + 3 + 2 + 2 + 1 + 1 + 1 + 1 = 26;
a(2) = [100/1]+[100/2]+[100/3]+[100/4]+[100/5]+[100/6]+[100/7]+[100/8]+[100/9] = 100 + 50 + 33 + 25 + 20 + 16 + 14 + 12 + 11 = 281.

Prog

(Python)
def a(n): return sum(10**n//k for k in range(1, 10))
print([a(n) for n in range(20)]) # Michael S. Branicky, Jan 26 2021
(PARI) a(n) = sum(k=1, 9, 10^n\k); \\ Michel Marcus, Jan 26 2021

Crossrefs

Cf. A055642, A130890.

Sequence in context: A006045 A022686 A200555 * A336732 A227332 A020925

Adjacent sequences: A130898 A130899 A130900 * A130902 A130903 A130904

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jun 08 2007

Status

approved