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A272068
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a(n) = (10^n-1)^5.
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5
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0, 59049, 9509900499, 995009990004999, 99950009999000049999, 9999500009999900000499999, 999995000009999990000004999999, 99999950000009999999000000049999999, 9999999500000009999999900000000499999999, 999999995000000009999999990000000004999999999, 99999999950000000009999999999000000000049999999999
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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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)
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EXAMPLE
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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)
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MAPLE
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MATHEMATICA
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PROG
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(Ruby)
(0..n).each{|i| p ('9' * i).to_i ** 5}
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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