A122121 Number of primes <= 10^(n/2).

0, 2, 4, 11, 25, 65, 168, 446, 1229, 3401, 9592, 27293, 78498, 227647, 664579, 1951957, 5761455, 17082666, 50847534, 151876932, 455052511, 1367199811, 4118054813, 12431880460, 37607912018, 113983535775, 346065536839, 1052370166553, 3204941750802, 9773865306521

Offset

0,2

Links

David Baugh, Table of n, a(n) for n = 0..52

Formula

a(2n) = A006880(n). - R. J. Mathar, Jan 13 2007

Example

a(3) = 11: sqrt(1000) = 31.62277660..., pi(31) = 11.

Mathematica

a={}; For[n=0, n<=27, n++, AppendTo[a, PrimePi[10^(n/2)]]]; Print[a]; (* John W. Layman, Mar 12 2010 *)

Prog

(PARI) { a= 0; n= 1; p=2 ; while(1, a++ ; pnext =nextprime(p+1) ; if( p^2 <= 10^n && pnext^2>10^n, print(a) ; n++ ; ) ; p=pnext ; ) ; } \\ R. J. Mathar, Jan 13 2007

Crossrefs

Cf. A000720, A006880.

Sequence in context: A329707 A071973 A086424 * A368412 A080009 A159336

Adjacent sequences: A122118 A122119 A122120 * A122122 A122123 A122124

Keyword

nonn

Author

N. J. A. Sloane, based on a suggestion from Klaus Kastberg (Kastberg(AT)aapt.net.au), Oct 17 2006

Extensions

More terms from R. J. Mathar, Jan 13 2007

a(0)-a(17) confirmed, and a(18)-a(26) added using Mathematica, by John W. Layman, Mar 12 2010

a(27) and a(28) added using Mathematica, by David Baugh, Oct 06 2011

a(29) from Donovan Johnson, Mar 12 2013

a(30)-a(46) added using Kim Walisch's primecount program, by David Baugh, Feb 10 2015

a(47)-a(52) from David Baugh using Kim Walisch's primecount program, Jun 19 2016

Status

approved