A272068 a(n) = (10^n-1)^5.

0, 59049, 9509900499, 995009990004999, 99950009999000049999, 9999500009999900000499999, 999995000009999990000004999999, 99999950000009999999000000049999999, 9999999500000009999999900000000499999999, 999999995000000009999999990000000004999999999, 99999999950000000009999999999000000000049999999999

Offset: 0

Author

Seiichi Manyama, Apr 19 2016

Keywords

• nonn
• easy

Comments

The sum of the digits of a(n) is divisible by 27. For example, 9^5 = 59049 and 5 + 9 + 0 + 4 + 9 = 27 * 1.

Number of 9 in a(n) is 3*n-1 for n > 0. - Seiichi Manyama, Sep 18 2018

Examples

			From _Seiichi Manyama_, Sep 18 2018: (Start)
n| a(n) can be divided into 5 parts for n > 1.
-+--------------------------------------------
1|        5    9    04    9
2|   9   50   99   004   99
3|  99  500  999  0004  999
4| 999 5000 9999 00004 9999
(End)
		

Links

• Index entries for linear recurrences with constant coefficients, signature (111111,-1122322110,1123333211000,-112232211000000,1111110000000000,-1000000000000000).

Crossrefs

Cf. A002283, A059988, A272066, A272067, A319358.

Programs

Magma

[(10^n-1)^5 : n in [0..10]]; // Wesley Ivan Hurt, Apr 19 2016

Maple

A272068:=n->(10^n-1)^5: seq(A272068(n), n=0..10); # Wesley Ivan Hurt, Apr 19 2016

Mathematica

(10^Range[0, 10] - 1)^5 (* Wesley Ivan Hurt, Apr 19 2016 *)

PARI

a(n) = (10^n-1)^5; \\ Michel Marcus, Apr 19 2016

Ruby

(0..n).each{|i| p ('9' * i).to_i ** 5}

Formula

a(n) = A002283(n)^5.

From Ilya Gutkovskiy, Apr 19 2016: (Start)

O.g.f.: 59049*x*(1 + 49940*x + 78366000*x^2 + 4994000000*x^3 + 10000000000*x^4)/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)*(1 - 10000*x)*(1 - 100000*x)).

E.g.f.: -exp(x) + 5*exp(10*x) - 10*exp(100*x) + 10*exp(1000*x) - 5*exp(10000*x) + exp(100000*x). (End)