|
|
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.
|
|
1
|
|
|
1, 5, 3, 25, 2, 16, 142857, 125, 1, 1, 9, 83, 76923, 714285, 6, 625, 588235294117647, 5, 52631578947368421, 5, 47619, 45, 434782608695652173913, 416, 4, 384615, 37, 3571428, 344827586206896551724137931, 3, 32258064516129, 3125, 3, 2941176470588235, 285714, 27
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
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).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(1) = 1 because 1/1 = 1.0 (k = 0),
a(2) = 5 because 1/2 = 0.5 (k = 1),
a(3) = 3 because 1/3 = 0.{3}*, where {...}* means that these digits repeat forever.
a(4) = 25 because 1/4 = 0.25 (k = 2),
a(5) = 2 because 1/5 = 0.2 (k = 1),
a(6) = 16 because 1/6 = 0.1{6}* (k = 2),
a(7) = 142857 because 1/7 = 0.{142857}* (k = 6),
a(8) = 125 because 1/8 = 0.125 (k = 3),
a(9) = 1 because 1/9 = 0.{1}* (k = 1),
a(10) = 1 because 1/10 = 0.1 (k = 1), ...
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|