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A037124 Numbers that contain only one nonzero digit.

%I A037124 #82 Oct 16 2024 22:26:11
%S A037124 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 A037124 700,800,900,1000,2000,3000,4000,5000,6000,7000,8000,9000,10000,20000,
%U A037124 30000,40000,50000,60000,70000,80000,90000,100000
%N A037124 Numbers that contain only one nonzero digit.
%C A037124 Starting with 1: next greater number not containing the highest digit (see also A098395). - _Reinhard Zumkeller_, Oct 31 2004
%C A037124 A061116 is a subsequence. - _Reinhard Zumkeller_, Mar 26 2008
%C A037124 Subsequence of A193460. - _Reinhard Zumkeller_, Jul 26 2011
%H A037124 Reinhard Zumkeller, <a href="/A037124/b037124.txt">Table of n, a(n) for n = 1..1000</a>
%H A037124 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 A037124 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A037124 a(n) = (((n - 1) mod 9) + 1) * 10^floor((n - 1)/9). E.g., a(40) = ((39 mod 9) + 1) * 10^floor(39/9) = (3 + 1) * 10^4 = 40000. - _Carl R. White_, Jan 08 2004
%F A037124 a(n) = A051885(n-1) + 1. - _Reinhard Zumkeller_, Jan 03 2008, Jul 10 2011
%F A037124 A138707(a(n)) = A000005(a(n)). - _Reinhard Zumkeller_, Mar 26 2008
%F A037124 From _Reinhard Zumkeller_, May 26 2008: (Start)
%F A037124 a(n+1) = a(n) + a(n - n mod 9).
%F A037124 a(n) = A140740(n+9, 9). (End)
%F A037124 A055640(a(n)) = 1. - _Reinhard Zumkeller_, May 03 2011
%F A037124 A193459(a(n)) = A000005(a(n)). - _Reinhard Zumkeller_, Jul 26 2011
%F A037124 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 A037124 a(n) = (10^floor((n - 1)/9))*(n - 9*floor((n - 1)/9)). - _José de Jesús Camacho Medina_, Nov 10 2014
%F A037124 From _Chai Wah Wu_, May 28 2016: (Start)
%F A037124 a(n) = 10*a(n-9).
%F A037124 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 A037124 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 A037124 Sum_{n>=1} 1/a(n) = 7129/2268. - _Amiram Eldar_, Jan 21 2022
%t A037124 Table[(10^Floor[(n - 1)/9])*(n - 9*Floor[(n - 1)/9]), {n, 1, 50}] (* _José de Jesús Camacho Medina_, Nov 10 2014 *)
%t A037124 Array[(Mod[#, 9] + 1) * 10^Floor[#/9] &, 50, 0] (* _Paolo Xausa_, Oct 10 2024 *)
%o A037124 (Haskell)
%o A037124 a037124 n = a037124_list !! (n-1)
%o A037124 a037124_list = f [1..9] where f (x:xs) = x : f (xs ++ [10*x])
%o A037124 -- _Reinhard Zumkeller_, May 03 2011
%o A037124 (Magma) [((n mod 9)+1) * 10^Floor(n/9): n in [0..50]]; // _Vincenzo Librandi_, Nov 11 2014
%o A037124 (PARI) is(n)=n>0 && n/10^valuation(n,10)<10 \\ _Charles R Greathouse IV_, Jan 29 2017
%o A037124 (Python)
%o A037124 def A037124(n):
%o A037124     a, b = divmod(n-1,9)
%o A037124     return 10**a*(b+1) # _Chai Wah Wu_, Oct 16 2024
%Y A037124 Cf. A000005, A000079, A011279, A038754, A051885, A055640, A061116, A133464, A138707, A140730, A140740, A193459, A193460.
%K A037124 nonn,base,easy
%O A037124 1,2
%A A037124 Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998