

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
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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.


REFERENCES

Freed, Edwin E. 1983. "Binary Magic Numbers," Dr. Dobb's Journal Vol. 78 (April), pp. 2437. Available from https://archive.org/details/dr_dobbs_journal_vol_08/page/n185/mode/2up


LINKS

Ray Chandler, Table of n, a(n) for n = 1..60
OEIS Wiki, Cyclic numbers
Eric Weisstein's World of Mathematics, Cyclic number
Wikipedia, Cyclic number


FORMULA

a(n) = (10^(A001913(n)1)  1) / A001913(n).


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.
The nth terms of A060284 where n is a member of A001913.
Sequence in context: A144504 A344436 A146754 * A004042 A145742 A236995
Adjacent sequences: A180337 A180338 A180339 * A180341 A180342 A180343


KEYWORD

base,nonn


AUTHOR

Ralph Kerchner (daxkerchner(AT)hotmail.com), Aug 28 2010


STATUS

approved



