A172500 Numerator of fraction whose decimal representation has form 0.(n)(n)(n)...with repeating part n.

1, 2, 1, 4, 5, 2, 7, 8, 1, 10, 1, 4, 13, 14, 5, 16, 17, 2, 19, 20, 7, 2, 23, 8, 25, 26, 3, 28, 29, 10, 31, 32, 1, 34, 35, 4, 37, 38, 13, 40, 41, 14, 43, 4, 5, 46, 47, 16, 49, 50, 17, 52, 53, 6, 5, 56, 19, 58, 59, 20, 61, 62, 7, 64, 65, 2, 67, 68, 23, 70, 71, 8, 73, 74, 25

Offset

1,2

Comments

a(n) is a divisor of n. - Robert G. Wilson v, Jul 04 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

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

Example

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

Maple

a:= n-> numer(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}, Numerator[n/(10^lg - 1)]]; Array[f, 75] (* Robert G. Wilson v, Jul 04 2015 *)

Prog

(Python)
from sympy import sympify
def A172500(n): return sympify('0.['+str(n)+']').p # Chai Wah Wu, Nov 12 2021

Crossrefs

Denominators in A172502.

Sequence in context: A343250 A065518 A072012 * A330355 A329424 A038502

Adjacent sequences: A172497 A172498 A172499 * A172501 A172502 A172503

Keyword

nonn,base

Author

Jaroslav Krizek, Feb 05 2010

Extensions

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

More terms from Robert G. Wilson v, Jul 04 2015

Status

approved