A078267 - OEIS

%I #26 Oct 08 2021 03:12:33

%S 10,5,10,5,2,5,10,5,10,10,100,25,100,50,20,25,100,50,100,5,100,50,100,

%T 25,4,50,100,25,100,10,100,25,100,50,20,25,100,50,100,5,100,50,100,25,

%U 20,50,100,25,100,2,100,25,100,50,20,25,100,50,100,5,100,50,100,25,20

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

%C From _Jaroslav Krizek_, Feb 05 2010: (Start)

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

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

%C (End)

%H Michael De Vlieger, <a href="/A078267/b078267.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = (A078268(n)*10^A055642(n)) / n. [_Jaroslav Krizek_, Feb 05 2010]

%F a(n) = 10^A055642(n)/gcd(n, 10^A055642(n)). - _Michael S. Branicky_, Oct 05 2021

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

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

%o (PARI) a(n) = denominator(n/10^(#Str(n))); \\ _Michel Marcus_, Mar 31 2019

%o (Python)

%o from math import gcd

%o def a(n): b = 10**len(str(n)); return b//gcd(n, b)

%o print([a(n) for n in range(1, 103)]) # _Michael S. Branicky_, Oct 05 2021

%Y Cf. A055642, A078268.

%K base,frac,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 24 2002

%E Edited and extended by _Henry Bottomley_, Dec 08 2002