cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A068542 Period of the fraction 1/3^n.

This page as a plain text file.
%I A068542 #12 Jul 23 2025 11:04:10
%S A068542 3,1,370,123456790,411522633744855967078189300,
%T A068542 137174211248285322359396433470507544581618655692729766803840877914951989026063100
%N A068542 Period of the fraction 1/3^n.
%C A068542 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
%H A068542 Robert Israel, <a href="/A068542/b068542.txt">Table of n, a(n) for n = 1..8</a>
%F A068542 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
%e A068542 1/3^3 = 0.0370370370..., hence a(3) = 370.
%p A068542 f:= proc(n) local k,v;
%p A068542     k:= numtheory:-order(10,3^n);
%p A068542     v:= (10^k-1)/3^n;
%p A068542     v * 10^(k-ilog10(v)-1)
%p A068542 end proc:
%p A068542 map(f, [$1..8]); # _Robert Israel_, Jul 23 2025
%o A068542 (PARI) apply( {A068542(n)=10^(3^max(n-2,0)+logint(3^n,10))\3^n}, [1..6]) \\ _M. F. Hasler_, Apr 23 2021
%K A068542 nonn
%O A068542 1,1
%A A068542 _Benoit Cloitre_, Mar 22 2002