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URL: https://oeis.org/A086018

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A086018
Number of cyclic numbers (A001913) <= 10^n.
3
0, 1, 9, 60, 467, 3617, 29500, 248881, 2155288, 19016617, 170169241, 1539964486, 14063663530, 129413160100
OFFSET
0,3
COMMENTS
Note that there are several different definitions of cyclic number: this sequence refers to A001913.
LINKS
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
Sequence in context: A153820 A390418 A009139 * A197402 A213133 A159037
KEYWORD
nonn,nice,more
AUTHOR
Eric W. Weisstein, Jul 07 2003
EXTENSIONS
a(11)-a(13) from Hiroaki Yamanouchi, Oct 10 2015
STATUS
approved