

A086018


Number of cyclic numbers (A001913) <= 10^n.


3



0, 1, 9, 60, 467, 3617, 29500, 248881, 2155288, 19016617, 170169241, 1539964486, 14063663530, 129413160100
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Note that there are several different definitions of cyclic number: this sequence refers to A001913.


LINKS

Table of n, a(n) for n=0..13.
Eric Weisstein's World of Mathematics, Cyclic Number
Eric Weisstein's World of Mathematics, Full Reptend Prime


FORMULA

Conjectured ratio a(n)/A006880(n) as n>infinity is Artin's constant 0.3739558136...


EXAMPLE

a(1)=1 since 7 is the only cyclic number <= 10^1.
a(2)=9 since the following are the cyclic numbers <= 10^2: 7, 17, 19, 23, 29, 47, 59, 61, 97.


MATHEMATICA

DigitCycleLength[ r_Rational, b_Integer?Positive ] := MultiplicativeOrder[ b, FixedPoint[ Quotient[ #, GCD[ #, b ] ] &, Denominator[ r ] ] ]; a = 0; Do[ If[ Prime[ n ]  DigitCycleLength[ 1/Prime[ n ], 10 ] == 1, a++ ], {n, 2, PrimePi[ 10^7 ]} ] Print[ a ]


CROSSREFS

Cf. A001913, A040402.
Sequence in context: A026785 A153820 A009139 * A197402 A213133 A159037
Adjacent sequences: A086015 A086016 A086017 * A086019 A086020 A086021


KEYWORD

nonn,nice,more


AUTHOR

Eric W. Weisstein, Jul 07 2003


EXTENSIONS

Extended by Farideh Firoozbakht, Jud McCranie, Ed Pegg Jr and Eric W. Weisstein, Aug 29 2003
a(11)a(13) from Hiroaki Yamanouchi, Oct 10 2015


STATUS

approved



