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A272067
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a(n) = (10^n-1)^4.
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5
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0, 6561, 96059601, 996005996001, 9996000599960001, 99996000059999600001, 999996000005999996000001, 9999996000000599999960000001, 99999996000000059999999600000001, 999999996000000005999999996000000001, 9999999996000000000599999999960000000001, 99999999996000000000059999999999600000000001
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graph;
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 18. For example, 9^4 = 6561 and 6 + 5 + 6 + 1 = 18 * 1.
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LINKS
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FORMULA
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O.g.f.: 6561*x*(1 + 100*x)*(1 + 3430*x + 10000*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)*(1 - 10000*x)).
E.g.f.: (1 - 4*exp(9*x) + 6*exp(99*x) - 4*exp(999*x) + exp(9999*x))*exp(x). (End)
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EXAMPLE
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n| a(n) can be divided into 4 parts for n > 1.
-+--------------------------------------------
1| 65 61
2| 9 605 9 601
3| 99 6005 99 6001
4| 999 60005 999 60001
(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 ** 4}
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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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