A037124 Numbers that contain only one nonzero digit.

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

Offset: 1

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998

Keywords

• nonn
• base
• easy

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.
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A000005, A000079, A011279, A038754, A051885, A055640, A061116, A133464, A138707, A140730, A140740, A193459, A193460.

Programs

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

Mathematica

Table[(10^Floor[(n - 1)/9])*(n - 9*Floor[(n - 1)/9]), {n, 1, 50}] (* José de Jesús Camacho Medina, Nov 10 2014 *)
Array[(Mod[#, 9] + 1) * 10^Floor[#/9] &, 50, 0] (* Paolo Xausa, Oct 10 2024 *)

PARI

is(n)=n>0 && n/10^valuation(n,10)<10 \\ Charles R Greathouse IV, Jan 29 2017

Python

def A037124(n):
    a, b = divmod(n-1,9)
    return 10**a*(b+1) # Chai Wah Wu, Oct 16 2024

Formula

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

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