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

1,1

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)

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A055642, A078268.

Sequence in context: A152611 A241146 A296420 * A083950 A045617 A158486

Adjacent sequences: A078264 A078265 A078266 * A078268 A078269 A078270

Keyword

base,frac,nonn

Author

Amarnath Murthy, Nov 24 2002

Extensions

Edited and extended by Henry Bottomley, Dec 08 2002

Status

approved