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A037124 Numbers that contain only one nonzero digit. 21
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
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
Sequence in context: A070958 A051596 A071061 * A273737 A201982 A166508
KEYWORD
nonn,base,easy
AUTHOR
Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)