A099801 PrimePi(2n+1), the number of primes less than or equal to 2n+1.

0, 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: 0

Author

N. J. A. Sloane, Nov 19 2004

Keywords

• nonn
• easy

Comments

If we drop a(0), for all numbers k(n) [k(n) = 4*ceiling(n/2) + (-1)^n] congruent to -1 or +1 (mod 4) starting with k(n) = {3,5,7,9,11,...}, a(k(n)) is the number of primes up to a(k(n)). - Daniel Forgues, Mar 01 2009

For n > 0, equals 1 (to account for the even prime 2 which is not congruent to -1 or +1 (mod 4)) + partial sums of A101264 (for n > 0). - Daniel Forgues, Mar 01 2009

Links

• Daniel Forgues, Table of n, a(n) for n = 0..49999

Crossrefs

Bisection of A000720.

Programs

Maple

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

Mathematica

Table[PrimePi[2*n + 1], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 02 2013 *)

Extensions

More terms from Emeric Deutsch, Apr 12 2005