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A037124
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Numbers that contain only one nonzero digit.
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17
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000
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OFFSET
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1,2
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COMMENTS
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Starting with 1: next greater number not containing the highest digit (see also A098395). - Reinhard Zumkeller, Oct 31 2004
a(n) = A140740(n+9, 9). - Reinhard Zumkeller, May 26 2008
A055640(a(n)) = 1. - Reinhard Zumkeller, May 03 2011
A193459(a(n)) = A000005(a(n)), subsequence of A193460.
Sum_{n>0} 1/a(n)^s = (10^s)*(Zeta(s) - Zeta(s,10))/(10^s-1), with (s>1). - Enrique Pérez Herrero, Feb 05 2013
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REFERENCES
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Maltenfort, Michael. "Characterizing Additive Systems." The American Mathematical Monthly 124.2 (2017): 132-148.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index entries for 10-automatic sequences.
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FORMULA
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a(n) = ((n mod 9) + 1) * 10^floor(n/9). E.g., a(39) = ((39 mod 9) + 1) * 10^floor(39/9) = (3 + 1) * 10^4 = 40000. - Carl R. White, Jan 08 2004
a(n) = A051885(n-1) + 1. - Reinhard Zumkeller, Jan 03 2008, Jul 10 2011
A138707(a(n)) = A000005(a(n)); A061116 is a subsequence. - Reinhard Zumkeller, Mar 26 2008
a(n+1) = a(n) + a(n - n mod 9). - Reinhard Zumkeller, May 26 2008
a(n) = (10^floor((n - 1)/9))*(n - 9*floor((n - 1)/9)). - José de Jesús Camacho Medina, Nov 10 2014
From Chai Wah Wu, May 28 2016: (Start)
a(n) = 10*a(n-9).
G.f.: x*(9*x^8 + 8*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/(1 - 10*x^9). (End)
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MATHEMATICA
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Table[(10^Floor[(n - 1)/9])*(n - 9*Floor[(n - 1)/9]), {n, 1, 50}](* José de Jesús Camacho Medina, Nov 10 2014 *)
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PROG
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(Haskell)
a037124 n = a037124_list !! (n-1)
a037124_list = f [1..9] where f (x:xs) = x : f (xs ++ [10*x])
-- Reinhard Zumkeller, May 03 2011
(MAGMA) [((n mod 9)+1) * 10^Floor(n/9): n in [0..50]]; // Vincenzo Librandi, Nov 11 2014
(PARI) is(n)=n>1 && n/10^valuation(n, 10)<10 \\ Charles R Greathouse IV, Jan 29 2017
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CROSSREFS
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Cf. A000079, A038754, A133464, A140730.
Sequence in context: A051596 A071061 * A273737 A201982 A166508 A223080
Adjacent sequences: A037121 A037122 A037123 * A037125 A037126 A037127
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KEYWORD
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nonn,base,easy
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AUTHOR
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Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998
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STATUS
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approved
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