

A086018


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


3



0, 1, 9, 60, 467, 3617, 29500, 248881, 2155288, 19016617, 170169241, 1539964486, 14063663530, 129413160100
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OFFSET

0,3


COMMENTS

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


LINKS



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



KEYWORD

nonn,nice,more


AUTHOR



EXTENSIONS



STATUS

approved



