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%I #32 Sep 08 2022 08:46:16
%S 0,59049,9509900499,995009990004999,99950009999000049999,
%T 9999500009999900000499999,999995000009999990000004999999,
%U 99999950000009999999000000049999999,9999999500000009999999900000000499999999,999999995000000009999999990000000004999999999,99999999950000000009999999999000000000049999999999
%N a(n) = (10^n-1)^5.
%C 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.
%C Number of 9 in a(n) is 3*n-1 for n > 0. - _Seiichi Manyama_, Sep 18 2018
%F a(n) = A002283(n)^5.
%F From _Ilya Gutkovskiy_, Apr 19 2016: (Start)
%F 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)).
%F 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)
%e From _Seiichi Manyama_, Sep 18 2018: (Start)
%e n| a(n) can be divided into 5 parts for n > 1.
%e -+--------------------------------------------
%e 1| 5 9 04 9
%e 2| 9 50 99 004 99
%e 3| 99 500 999 0004 999
%e 4| 999 5000 9999 00004 9999
%e (End)
%p A272068:=n->(10^n-1)^5: seq(A272068(n), n=0..10); # _Wesley Ivan Hurt_, Apr 19 2016
%t (10^Range[0, 10] - 1)^5 (* _Wesley Ivan Hurt_, Apr 19 2016 *)
%o (Ruby)
%o (0..n).each{|i| p ('9' * i).to_i ** 5}
%o (PARI) a(n) = (10^n-1)^5; \\ _Michel Marcus_, Apr 19 2016
%o (Magma) [(10^n-1)^5 : n in [0..10]]; // _Wesley Ivan Hurt_, Apr 19 2016
%Y Cf. A002283, A059988, A272066, A272067, A319358.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Apr 19 2016
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