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, 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

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

a(n) = numerator(pi(n)/(n-pi(n))) = numerator(A000720(n)/A062298(n)). - Jason Yuen, Aug 31 2024

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) }
(PARI) a(n)=numerator(primepi(n)/(n-primepi(n))) \\ Jason Yuen, Aug 31 2024

Crossrefs

Cf. A000720, A062298.

Sequence in context: A324392 A340273 A029234 * A097019 A262999 A324933

Adjacent sequences: A102610 A102611 A102612 * A102614 A102615 A102616

Keyword

frac,nonn,easy

Author

Cino Hilliard, Jan 30 2005

Status

approved