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%I #17 Oct 10 2015 03:50:23
%S 0,1,9,60,467,3617,29500,248881,2155288,19016617,170169241,1539964486,
%T 14063663530,129413160100
%N Number of cyclic numbers (A001913) <= 10^n.
%C Note that there are several different definitions of cyclic number: this sequence refers to A001913.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclicNumber.html">Cyclic Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FullReptendPrime.html">Full Reptend Prime</a>
%F Conjectured ratio a(n)/A006880(n) as n->infinity is Artin's constant 0.3739558136...
%e a(1)=1 since 7 is the only cyclic number <= 10^1.
%e a(2)=9 since the following are the cyclic numbers <= 10^2: 7, 17, 19, 23, 29, 47, 59, 61, 97.
%t 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 ]
%Y Cf. A001913, A040402.
%K nonn,nice,more
%O 0,3
%A _Eric W. Weisstein_, Jul 07 2003
%E Extended by _Farideh Firoozbakht_, _Jud McCranie_, _Ed Pegg Jr_ and _Eric W. Weisstein_, Aug 29 2003
%E a(11)-a(13) from _Hiroaki Yamanouchi_, Oct 10 2015
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