|
|
A086018
|
|
Number of cyclic numbers (A001913) <= 10^n.
|
|
3
|
|
|
0, 1, 9, 60, 467, 3617, 29500, 248881, 2155288, 19016617, 170169241, 1539964486, 14063663530, 129413160100
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Note that there are several different definitions of cyclic number: this sequence refers to A001913.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,nice,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|