This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086018 #18 Feb 16 2025 08:32:50
%S A086018 0,1,9,60,467,3617,29500,248881,2155288,19016617,170169241,1539964486,
%T A086018 14063663530,129413160100
%N A086018 Number of cyclic numbers (A001913) <= 10^n.
%C A086018 Note that there are several different definitions of cyclic number: this sequence refers to A001913.
%H A086018 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CyclicNumber.html">Cyclic Number</a>
%H A086018 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FullReptendPrime.html">Full Reptend Prime</a>
%F A086018 Conjectured ratio a(n)/A006880(n) as n->infinity is Artin's constant 0.3739558136...
%e A086018 a(1)=1 since 7 is the only cyclic number <= 10^1.
%e A086018 a(2)=9 since the following are the cyclic numbers <= 10^2: 7, 17, 19, 23, 29, 47, 59, 61, 97.
%t A086018 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 A086018 Cf. A001913, A040402.
%K A086018 nonn,nice,more
%O A086018 0,3
%A A086018 _Eric W. Weisstein_, Jul 07 2003
%E A086018 Extended by _Farideh Firoozbakht_, _Jud McCranie_, _Ed Pegg Jr_ and _Eric W. Weisstein_, Aug 29 2003
%E A086018 a(11)-a(13) from _Hiroaki Yamanouchi_, Oct 10 2015