A105149 - OEIS

%I #8 Feb 05 2018 02:54:17

%S 0,1,1,2,1,2,2,2,1,3,2,3,3,2,4,2,3,3,4,5,1,6,3,5,3,4,4,5,4,6,5,5,3,6,

%T 5,7,6,4,6,5,7,6,5,6,6,8,8,5,6,8,7,6,5,9,9,7,10,6,7,8,5,10,6,10,9,8,8,

%U 10,8,11,5,9,9,13,10,9,9,9,8,8,10,12,7,11,12,12,10,10,12,10,12,10,10,10,11

%N Number of even semiprimes k such that n^2 < k <= (n+1)^2.

%C a(n)>=1 because there is always a number 2*prime(i) between n^2 and (n+1)^2 for n>0.

%H Robert Israel, <a href="/A105149/b105149.txt">Table of n, a(n) for n = 0..9999</a>

%e a(6)=2 because between 5^2 and 6^2 there are two 2*prime(i): 2*prime(6)=2*13 and 2*prime(7)=2*17.

%p L:= map(numtheory:-pi, [seq(floor(n^2/2),n=0..100)]):

%p L[2..-1]-L[1..-2]; # _Robert Israel_, Feb 04 2018

%t f[n_] := PrimePi[Floor[n^2/2]]; Table[f[(n + 1)] - f[n], {n, 0, 100}]

%Y Cf. A105148.

%K easy,nonn

%O 0,4

%A _Giovanni Teofilatto_, Apr 10 2005

%E Edited and extended by _Ray Chandler_, Apr 16 2005