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%I #72 Jan 21 2022 05:07:27
%S 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100,200,300,400,500,600,
%T 700,800,900,1000,2000,3000,4000,5000,6000,7000,8000,9000,10000,20000,
%U 30000,40000,50000,60000,70000,80000,90000,100000
%N Numbers that contain only one nonzero digit.
%C Starting with 1: next greater number not containing the highest digit (see also A098395). - _Reinhard Zumkeller_, Oct 31 2004
%C A061116 is a subsequence. - _Reinhard Zumkeller_, Mar 26 2008
%C Subsequence of A193460. - _Reinhard Zumkeller_, Jul 26 2011
%H Reinhard Zumkeller, <a href="/A037124/b037124.txt">Table of n, a(n) for n = 1..1000</a>
%H Michael Maltenfort, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.124.2.132">Characterizing Additive Systems</a>, The American Mathematical Monthly, Vol. 124, No. 2 (2017), pp. 132-148.
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F 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
%F a(n) = A051885(n-1) + 1. - _Reinhard Zumkeller_, Jan 03 2008, Jul 10 2011
%F A138707(a(n)) = A000005(a(n)). - _Reinhard Zumkeller_, Mar 26 2008
%F From _Reinhard Zumkeller_, May 26 2008: (Start)
%F a(n+1) = a(n) + a(n - n mod 9).
%F a(n) = A140740(n+9, 9). (End)
%F A055640(a(n)) = 1. - _Reinhard Zumkeller_, May 03 2011
%F A193459(a(n)) = A000005(a(n)). - _Reinhard Zumkeller_, Jul 26 2011
%F 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
%F a(n) = (10^floor((n - 1)/9))*(n - 9*floor((n - 1)/9)). - _José de Jesús Camacho Medina_, Nov 10 2014
%F From _Chai Wah Wu_, May 28 2016: (Start)
%F a(n) = 10*a(n-9).
%F 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)
%F 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
%F Sum_{n>=1} 1/a(n) = 7129/2268. - _Amiram Eldar_, Jan 21 2022
%t Table[(10^Floor[(n - 1)/9])*(n - 9*Floor[(n - 1)/9]), {n, 1, 50}](* _José de Jesús Camacho Medina_, Nov 10 2014 *)
%o (Haskell)
%o a037124 n = a037124_list !! (n-1)
%o a037124_list = f [1..9] where f (x:xs) = x : f (xs ++ [10*x])
%o -- _Reinhard Zumkeller_, May 03 2011
%o (Magma) [((n mod 9)+1) * 10^Floor(n/9): n in [0..50]]; // _Vincenzo Librandi_, Nov 11 2014
%o (PARI) is(n)=n>0 && n/10^valuation(n,10)<10 \\ _Charles R Greathouse IV_, Jan 29 2017
%Y Cf. A000005, A000079, A011279, A038754, A051885, A055640, A061116, A133464, A138707, A140730, A140740, A193459, A193460.
%K nonn,base,easy
%O 1,2
%A Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998
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