|
|
A180340
|
|
Numbers with x digits such that the first x multiples are cyclic permutations of the number, leading 0's omitted (or cyclic numbers).
|
|
3
|
|
|
142857, 588235294117647, 52631578947368421, 434782608695652173913, 344827586206896551724137931, 212765957446808510638297872340425531914893617, 169491525423728813559322033898305084745762711864406779661
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Periodic part of decimal expansion of 1/A001913(n). The number of digits in each term (including leading zeros), plus one, makes the sequence A001913.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
142857 is in the sequence because it has 6 digits and the first 6 multiples of 142857 are 142857, 285714, 428571, 571428, 714285, and 857142, all cyclic permutations of the number. Also the first term of A001913 is 7, and 1/7 = 0.142857142857... .
588235294117647 is the next number because 0588235294117647 has 16 digits and the first 16 multiples are cyclic permutations of the number; the second term of A001913 is 17, and 1/17 = 0.05882352941176470588235294117647... .
|
|
MATHEMATICA
|
Map[(10^(# - 1) - 1)/# &, Select[Prime@ Range@ 17, MultiplicativeOrder[10, #] == # - 1 &]] (* Michael De Vlieger, Apr 03 2017 *)
|
|
CROSSREFS
|
A006883 starting from the second term of A006883, omitting ending 0's.
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
Ralph Kerchner (daxkerchner(AT)hotmail.com), Aug 28 2010
|
|
STATUS
|
approved
|
|
|
|