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A217094
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Least index k such that A011540(k) >= 10^n.
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7
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2, 2, 11, 182, 2621, 33572, 402131, 4619162, 51572441, 564151952, 6077367551, 64696307942, 682266771461, 7140400943132, 74263608488171, 768372476393522, 7915352287541681, 81238170587875112, 831143535290875991, 8480291817617883902, 86322626358560955101
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OFFSET
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0,1
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COMMENTS
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For n>0 also index k such that A011540(k) = 10^n.
For n>1: A011540(a(n)) is the least number with n zero digits.
For n>0: a(n) - 1 is the number of numbers with <= n digits which contain the digit '0'. - Hieronymus Fischer, Dec 27 2013
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LINKS
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FORMULA
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a(n+1) = 10*a(n) - 9*a(n-1) + 9*10^(n-1), n>0.
a(n) = 2 + 10^n - 9^n - (9^n - 1)/8.
G.f.: (189*x^2 - 38*x + 2)/((1-x)*(1-9*x)*(1-10*x)).
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EXAMPLE
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a(0) = 2, since A011540(2) = 10 >= 10^0.
a(1) = 2, since A011540(2) = 10 >= 10^1.
a(2) = 11, since A011540(11) = 100 >= 10^2, but A011540(10) = 90 < 10^2.
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MATHEMATICA
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LinearRecurrence[{20, -109, 90}, {2, 2, 11}, 30] (* Harvey P. Dale, Aug 02 2015 *)
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PROG
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(PARI) for(n=0, 50, print1(2 +10^n -9^n -(9^n -1)/8, ", ")) \\ G. C. Greubel, Apr 18 2018
(Magma) [2 +10^n -9^n -(9^n -1)/8: n in [0..50]]; // G. C. Greubel, Apr 18 2018
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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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