A172502 Denominator of fraction whose decimal representation has form 0.(n)(n)(n)...with repeating part n.

9, 9, 3, 9, 9, 3, 9, 9, 1, 99, 9, 33, 99, 99, 33, 99, 99, 11, 99, 99, 33, 9, 99, 33, 99, 99, 11, 99, 99, 33, 99, 99, 3, 99, 99, 11, 99, 99, 33, 99, 99, 33, 99, 9, 11, 99, 99, 33, 99, 99, 33, 99, 99, 11, 9, 99, 33, 99, 99, 33, 99, 99, 11, 99, 99, 3, 99, 99, 33

Offset

1,1

Comments

a(n) is a divisor of 10^(floor(1+log_10(n)))-1. - Robert G. Wilson v, Jul 04 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 1..9999

Formula

a(n) = denominator of n/(10^floor(1+log_10(n))-1) in reduced terms. - Robert G. Wilson v, Jul 05 2015

Example

a(10) = 99; 10 / 99 = 0.10101010... (repeating 10). a(9) = 1; 1 / 1 = 0.9999999...

Maple

a:= n-> denom(n*sum(10^(-i*length(n)), i=1..infinity)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 04 2015

Mathematica

f[n_] := Block[{lg = 1 + Floor@ Log10@ n}, Denominator[n/(10^lg - 1)]]; Array[f, 70] (* Robert G. Wilson v, Jul 04 2015 *)

Prog

(Python)
from sympy import sympify
def A172502(n): return sympify('0.['+str(n)+']').q # Chai Wah Wu, Nov 12 2021
(PARI) a(n) = my(qd = #digits(n)); denominator(n / (10^(qd)-1)); \\ Michel Marcus, Jul 29 2023

Crossrefs

Numerators are in A172500.

Sequence in context: A007471 A180012 A172504 * A118739 A192031 A283749

Adjacent sequences: A172499 A172500 A172501 * A172503 A172504 A172505

Keyword

nonn,base

Author

Jaroslav Krizek, Feb 05 2010

Extensions

Edited by Franklin T. Adams-Watters, Mar 28 2014

More terms from Alois P. Heinz, Jul 04 2015

Status

approved