A078267 Smallest k such that k*N is an integer where N is obtained by placing the string "n" after a decimal point.

10, 5, 10, 5, 2, 5, 10, 5, 10, 10, 100, 25, 100, 50, 20, 25, 100, 50, 100, 5, 100, 50, 100, 25, 4, 50, 100, 25, 100, 10, 100, 25, 100, 50, 20, 25, 100, 50, 100, 5, 100, 50, 100, 25, 20, 50, 100, 25, 100, 2, 100, 25, 100, 50, 20, 25, 100, 50, 100, 5, 100, 50, 100, 25, 20

Offset: 1

Author

Amarnath Murthy, Nov 24 2002

Keywords

• base
• frac
• nonn

Comments

From Jaroslav Krizek, Feb 05 2010: (Start)

a(n) is the denominator of fraction a/b, where gcd(a, b) = 1, such that its decimal representation has form 0.(n).

The numerators are in A078268. Example: a(6) = 5; 3/5 = 0.6.

(End)

Examples

			a(40) = 5 since 5*0.40 = 2 is an integer. a(1) = a(10) = 10.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055642, A078268.

Programs

Mathematica

Array[#2/GCD[#1, #2] & @@ {#, 10^IntegerLength[#]} &, 65] (* Michael De Vlieger, Oct 05 2021 *)

PARI

a(n) = denominator(n/10^(#Str(n))); \\ Michel Marcus, Mar 31 2019

Python

from math import gcd
def a(n): b = 10**len(str(n)); return b//gcd(n, b)
print([a(n) for n in range(1, 103)]) # Michael S. Branicky, Oct 05 2021

Formula

a(10^m) = 10, a(r*10^m) = a(r).

a(n) = (A078268(n)*10^A055642(n)) / n. [Jaroslav Krizek, Feb 05 2010]

a(n) = 10^A055642(n)/gcd(n, 10^A055642(n)). - Michael S. Branicky, Oct 05 2021

Extensions

Edited and extended by Henry Bottomley, Dec 08 2002