cp's OEIS Frontend

A266385 a(n) = floor(10^k/n) where k is the smallest integer such that the whole first period or the whole terminating fractional part of the decimal expansion of 1/n is shifted to appear before the decimal point in 10^k/n.

%I A266385 #22 Jun 06 2021 11:54:21
%S A266385 1,5,3,25,2,16,142857,125,1,1,9,83,76923,714285,6,625,588235294117647,
%T A266385 5,52631578947368421,5,47619,45,434782608695652173913,416,4,384615,37,
%U A266385 3571428,344827586206896551724137931,3,32258064516129,3125,3,2941176470588235,285714,27
%N A266385 a(n) = floor(10^k/n) where k is the smallest integer such that the whole first period or the whole terminating fractional part of the decimal expansion of 1/n is shifted to appear before the decimal point in 10^k/n.
%C A266385 The period is given in A051626 (with 0 if 1/n terminates) and A007732 (with 1 if 1/n terminates). The periodic part is given in A060284 (with initial 0's omitted) and A036275 (with initial 0's appended).
%H A266385 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>
%F A266385 a(n) = A060284(n) (mod 10^A051626(n)).
%e A266385 a(1) = 1 because 1/1 = 1.0 (k = 0),
%e A266385 a(2) = 5 because 1/2 = 0.5 (k = 1),
%e A266385 a(3) = 3 because 1/3 = 0.{3}*, where {...}* means that these digits repeat forever.
%e A266385 a(4) = 25 because 1/4 = 0.25 (k = 2),
%e A266385 a(5) = 2 because 1/5 = 0.2 (k = 1),
%e A266385 a(6) = 16 because 1/6 = 0.1{6}* (k = 2),
%e A266385 a(7) = 142857 because 1/7 = 0.{142857}* (k = 6),
%e A266385 a(8) = 125 because 1/8 = 0.125 (k = 3),
%e A266385 a(9) = 1 because 1/9 = 0.{1}* (k = 1),
%e A266385 a(10) = 1 because 1/10 = 0.1 (k = 1), ...
%Y A266385 Cf. A036275, A051626, A060284, A007732.
%K A266385 nonn,base,easy
%O A266385 1,2
%A A266385 _M. F. Hasler_, Dec 28 2015
%E A266385 Name edited and a(13) onwards from _Mohammed Yaseen_, Jun 03 2021