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A328683
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Positive integers that are equal to 99...99 (repdigit with n digits 9) times the sum of their digits.
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1
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81, 1782, 26973, 359964, 4499955, 53999946, 629999937, 7199999928, 80999999919, 899999999910, 9899999999901, 107999999999892, 1169999999999883, 12599999999999874, 134999999999999865, 1439999999999999856, 15299999999999999847, 161999999999999999838
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OFFSET
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1,1
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COMMENTS
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The idea of this sequence comes from a problem during the annual Moscow Mathematical Olympiad (MMO) in 2001 (see reference).
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REFERENCES
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Roman Fedorov, Alexei Belov, Alexander Kovaldzhi, Ivan Yashchenko, Moscow Mathematical Olympiads, 2000-2005, Level B, Problem 5, 2001, MSRI, 2011, p. 8 and 70/71.
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LINKS
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FORMULA
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a(n) = 9 * n * (10^n - 1).
G.f.: 81*x*(1 - 10*x^2) / ((1 - x)^2*(1 - 10*x)^2).
a(n) = 22*a(n-1) - 141*a(n-2) + 220*a(n-3) - 100*a(n-4) for n>4.
(End)
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EXAMPLE
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359964 = 36 * 9999 and the digital sum of 359964 = 36 , so 359964 = a(4).
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MAPLE
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C:=seq(9*n*(10^n-1), n=1..20);
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MATHEMATICA
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Table[9*n*(10^n - 1), {n, 1, 18}] (* Amiram Eldar, Feb 25 2020 *)
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PROG
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(PARI) Vec(81*x*(1 - 10*x^2) / ((1 - x)^2*(1 - 10*x)^2) + O(x^20)) \\ Colin Barker, Feb 25 2020
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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