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A037124 Numbers that contain only one nonzero digit. 15
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

a(n) = A140740(n+9,9). - Reinhard Zumkeller, May 26 2008

A055640(a(n)) = 1. [Reinhard Zumkeller, May 03 2011]

A193459(a(n)) = A000005(a(n)), subsequence of A193460.

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

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)); A061116 is a subsequence. - Reinhard Zumkeller, Mar 26 2008

a(n+1) = a(n) + a(n - n mod 9). - Reinhard Zumkeller, May 26 2008

a(n) = (10^floor((n - 1)/9))*(n - 9*floor((n - 1)/9)). - José de Jesús Camacho Medina, Nov 10 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 *)

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

CROSSREFS

Cf. A000079, A038754, A133464, A140730.

Sequence in context: A070958 A051596 A071061 * A201982 A166508 A223080

Adjacent sequences:  A037121 A037122 A037123 * A037125 A037126 A037127

KEYWORD

nonn,base

AUTHOR

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

STATUS

approved

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Last modified November 25 23:15 EST 2014. Contains 250015 sequences.