A111114 Integer part of prime(n)/pi(n).

3, 2, 3, 3, 4, 4, 4, 5, 7, 6, 7, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 11, 11, 11, 10, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 14, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 15, 16, 17, 17, 17, 17, 17, 17, 18, 18, 17, 17, 17, 17, 18, 18, 18, 18

Offset

2,1

Comments

Conjecture: As n -> infinity, there are infinitely many n's such that a(n) is greater than a(n+1).

a(n) > a(n + 1) only if n + 1 is prime. - David A. Corneth, Aug 22 2020

Links

Harry J. Smith, Table of n, a(n) for n = 2..10000

Example

a(2) = 3 as prime(2) = 3, pi(2) = 1 so a(2) = floor(3/1) = 3.
a(3) = 2 as prime(3) = 5, pi(3) = 2 so a(3) = floor(5/2) = 2.

Mathematica

Table[IntegerPart[Prime[n]/PrimePi[n]], {n, 2, 80}] (* Harvey P. Dale, Nov 19 2014 *)

Prog

(PARI) a(n) = prime(n)\primepi(n)
(PARI) first(n) = {my(res = vector(n), t = 2, pit = 1); forprime(p = 3, oo, res[t-1] = p \ pit; if(t > n, return(res) ); t++; if(isprime(t), pit++ ) ) } \\ David A. Corneth, Aug 22 2020

Crossrefs

Cf. A000040 (primes), A000720 (pi).

Sequence in context: A260195 A061266 A345755 * A242409 A317623 A286244

Adjacent sequences: A111111 A111112 A111113 * A111115 A111116 A111117

Keyword

nonn,easy

Author

Cino Hilliard, Oct 14 2005

Status

approved