A090668 a(n)=[prime(n)*(n-pi(n))/(pi(n)+1)], where pi=A000720, [x]=floor(x).

2, 1, 1, 4, 5, 9, 10, 15, 23, 34, 31, 43, 41, 49, 60, 75, 73, 83, 81, 94, 105, 122, 116, 133, 155, 171, 185, 203, 188, 205, 211, 229, 251, 266, 298, 314, 301, 326, 346, 372, 358, 374, 369, 386, 407, 424, 422, 459, 482, 500, 524, 552, 524, 561, 589, 618, 648, 669

Offset

1,1

Comments

A sequence based on the ratios of distributions of primes and composite numbers.

By adding one to the distribution of primes function an initial n=1 singularity is avoided.

Links

Table of n, a(n) for n=1..58.

Formula

Asymptotically, a(n) ~ prime(n)*n/pi(n). - M. F. Hasler, Apr 06 2009

r[n_]=(1+PrimePi[n])/(n-PrimePi[n]) a(n) = Floor[(1/r[n])*Prime[n]]

Mathematica

d=237 r[n_]=(1+PrimePi[n])/(n-PrimePi[n]) aa=Table[Floor[(1/r[n])*Prime[n]], {n, 1, d}]

Prog

(PARI) A090668(n)=prime(n)*(n-primepi(n))\(primepi(n)+1) \\ M. F. Hasler, Apr 06 2009

Crossrefs

Sequence in context: A329689 A270952 A143392 * A307977 A355334 A295259

Adjacent sequences: A090665 A090666 A090667 * A090669 A090670 A090671

Keyword

nonn

Author

Roger L. Bagula, Dec 16 2003

Extensions

Edited by M. F. Hasler, Apr 07 2009

Status

approved