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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
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; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..86.

FORMULA

pi(n) is the number of primes <= n. Number of composites <= n = n - pi(n).

PROG

(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: A324392 A340273 A029234 * A097019 A262999 A324933

Adjacent sequences: A102610 A102611 A102612 * A102614 A102615 A102616

KEYWORD

frac,nonn

AUTHOR

Cino Hilliard, Jan 30 2005

STATUS

approved

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Last modified November 30 05:38 EST 2022. Contains 358431 sequences. (Running on oeis4.)