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 A037124 Numbers that contain only one nonzero digit. 18
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Starting with 1: next greater number not containing the highest digit (see also A098395). - Reinhard Zumkeller, Oct 31 2004 A061116 is a subsequence. - Reinhard Zumkeller, Mar 26 2008 Subsequence of A193460. - Reinhard Zumkeller, Jul 26 2011 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Michael Maltenfort, Characterizing Additive Systems, The American Mathematical Monthly, Vol. 124, No. 2 (2017), pp. 132-148. FORMULA 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)). - Reinhard Zumkeller, Mar 26 2008 From Reinhard Zumkeller, May 26 2008: (Start) a(n+1) = a(n) + a(n - n mod 9). a(n) = A140740(n+9, 9). (End) A055640(a(n)) = 1. - Reinhard Zumkeller, May 03 2011 A193459(a(n)) = A000005(a(n)). - Reinhard Zumkeller, Jul 26 2011 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 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) a(n) ≍ 1.2589...^n, where the constant is A011279. (f ≍ g when f << g and g << f, that is, there are absolute constants c,C > 0 such that for all large n, |f(n)| <= c|g(n)| and |g(n)| <= C|f(n)|.) - Charles R Greathouse IV, Mar 11 2021 Sum_{n>=1} 1/a(n) = 7129/2268. - Amiram Eldar, Jan 21 2022 MATHEMATICA Table[(10^Floor[(n - 1)/9])*(n - 9*Floor[(n - 1)/9]), {n, 1, 50}](* José de Jesús Camacho Medina, Nov 10 2014 *) PROG (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>0 && n/10^valuation(n, 10)<10 \\ Charles R Greathouse IV, Jan 29 2017 CROSSREFS Cf. A000005, A000079, A011279, A038754, A051885, A055640, A061116, A133464, A138707, A140730, A140740, A193459, A193460. Sequence in context: A070958 A051596 A071061 * A273737 A201982 A166508 Adjacent sequences:  A037121 A037122 A037123 * A037125 A037126 A037127 KEYWORD nonn,base,easy AUTHOR Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998 STATUS approved

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Last modified May 25 09:45 EDT 2022. Contains 354066 sequences. (Running on oeis4.)