A099802 Bisection of A000720.

1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 11, 11, 11, 12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 30, 30, 30, 30, 30, 31, 31, 32, 32, 32, 33, 34, 34, 34, 34, 34

Offset

1,2

Comments

Maximal number of primes possible in a string of 2n consecutive numbers. - Lekraj Beedassy, Dec 04 2004

a(n) = A139325(n,1) + 1. - Reinhard Zumkeller, Apr 14 2008

Or the number of primes <= 2n. - Juri-Stepan Gerasimov, Oct 29 2009

Links

Robert Price, Table of n, a(n) for n = 1..5000

Formula

a(n) = A000720(n) + A035250(n) - A010051(n). - Reinhard Zumkeller, Jul 05 2010

a(n) = A000720(2*n). - Wesley Ivan Hurt, Jun 16 2013

Maple

with(numtheory):seq(pi(2*n), n=1..86); # Emeric Deutsch, Apr 12 2005

Mathematica

Table[PrimePi[2 n], {n, 1, 100}] (* Robert Price, Oct 31 2025 *)

Prog

(SageMath) [prime_pi(2*n) for n in range(1, 75)] # Zerinvary Lajos, Jun 06 2009
(PARI) a(n)=primepi(2*n) \\ Charles R Greathouse IV, Sep 02 2015

Crossrefs

Cf. A000720, A099801.

Cf. A028334 (run lengths).

Sequence in context: A316627 A377972 A099801 * A196266 A340792 A112232

Adjacent sequences: A099799 A099800 A099801 * A099803 A099804 A099805

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 19 2004

Extensions

More terms from Emeric Deutsch, Apr 12 2005

Status

approved