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Search: id:A086018
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| 0, 1, 9, 60, 467, 3617, 29500, 248881, 2155288, 19016617, 170169241
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Note that there are several different definitions of cyclic number: this sequence refers to A001913.
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LINKS
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Eric Weisstein's World of Mathematics, Cyclic Number
Eric Weisstein's World of Mathematics, Full Reptend Prime
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FORMULA
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Conjectured ratio a(n)/A006880(n) as n->infinity is Artin's constant 0.3739558136...
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EXAMPLE
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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.
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MATHEMATICA
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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 ]
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CROSSREFS
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Cf. A001913, A040402.
Sequence in context: A026785 A153820 A009139 this_sequence A159037 A138589 A058777
Adjacent sequences: A086015 A086016 A086017 this_sequence A086019 A086020 A086021
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KEYWORD
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nonn,nice
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jul 07, 2003
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EXTENSIONS
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Extended by Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Jud McCranie (j.mccranie(AT)comcast.net), Ed. Pegg Jr. (edp(AT)wolfram.com) and Eric Weisstein, Aug 29, 2003
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