|
Search: id:A102613
|
|
|
| A102613 |
|
Numerator of the reduced fractions of the ratios of the number of primes less than n over the number of composites less than n. |
|
+0
1
|
|
| 0, 1, 2, 1, 3, 1, 4, 1, 4, 2, 5, 5, 6, 3, 2, 3, 7, 7, 8, 2, 8, 4, 9, 3, 9, 9, 1, 9, 10, 1, 11, 11, 1, 11, 11, 11, 12, 6, 4, 3, 13, 13, 14, 7, 14, 7, 15, 5, 15, 3, 5, 15, 16, 8, 16, 2, 16, 8, 17, 17, 18, 9, 2, 9, 18, 3, 19, 19, 19, 19, 20, 5, 21, 21, 7, 21, 3, 7, 22, 11, 22, 11, 23, 23, 23, 23
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Conjecture: The ratio Pi(x)/(n-Pi(x)) tends to 0 as n tends to infinity. This is evident from the fact that Li(x)/((n-Li(x)) -> 0 as n -> infinity but unfortunately not proof.
|
|
FORMULA
|
pi(n) is the number of primes <= n. Number of composites <= n = n - pi(n).
|
|
PROGRAM
|
(PARI) pixovcmpx(n) = for(x=1, n, print1(numerator(pi(x)/(x-pi(x)))", ")) pi(n) = \Number of primes less than or equal to n. { local(c, x); c=0; forprime(x=1, n, c++); return(c) }
|
|
CROSSREFS
|
Sequence in context: A064839 A094741 A029234 this_sequence A097019 A085343 A049077
Adjacent sequences: A102610 A102611 A102612 this_sequence A102614 A102615 A102616
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Jan 30 2005
|
|
|
Search completed in 0.002 seconds
|
