A068542 Period of the fraction 1/3^n.

3, 1, 370, 123456790, 411522633744855967078189300, 137174211248285322359396433470507544581618655692729766803840877914951989026063100

Offset: 1

Author

Benoit Cloitre, Mar 22 2002

Keywords

• nonn

Comments

The length of the period is the number of digits of a(n): 1, 1, 3, 9, 27, 81, ... The terms a(n) are more precisely the integers made from the digits of a period, starting with the first nonzero digit. - M. F. Hasler, Apr 23 2021

Examples

			1/3^3 = 0.0370370370..., hence a(3) = 370.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..8

Programs

Maple

f:= proc(n) local k,v;
    k:= numtheory:-order(10,3^n);
    v:= (10^k-1)/3^n;
    v * 10^(k-ilog10(v)-1)
end proc:
map(f, [$1..8]); # Robert Israel, Jul 23 2025

PARI

apply( {A068542(n)=10^(3^max(n-2,0)+logint(3^n,10))\3^n}, [1..6]) \\ M. F. Hasler, Apr 23 2021

Formula

a(n) = floor(10^(3^max(n-2,0)+L(3^n))/3^n) where L(m) = floor(log10(m)). - M. F. Hasler, Apr 23 2021