A086018 Number of cyclic numbers (A001913) <= 10^n.

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

Offset: 0

Author

Eric W. Weisstein, Jul 07 2003

Keywords

• nonn
• nice
• more

Comments

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

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Cyclic Number
• Eric Weisstein's World of Mathematics, Full Reptend Prime

Crossrefs

Cf. A001913, A040402.

Programs

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 ]

Formula

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

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