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
Keywords
Examples
a(3) = 11: sqrt(1000) = 31.62277660..., pi(31) = 11.
Links
- David Baugh, Table of n, a(n) for n = 0..52
Programs
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Mathematica
a={}; For[n=0, n<=27, n++, AppendTo[a,PrimePi[10^(n/2)]]]; Print[a]; (* John W. Layman, Mar 12 2010 *) -
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 -
Python
from math import isqrt from sympy import primepi def A122121(n): return primepi(isqrt(10**n)) # Chai Wah Wu, Oct 17 2024
Formula
a(2n) = A006880(n). - R. J. Mathar, Jan 13 2007
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