A105149 Number of even semiprimes k such that n^2 < k <= (n+1)^2.

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, 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, 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

Offset

0,4

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 0..9999

Example

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.

Maple

L:= map(numtheory:-pi, [seq(floor(n^2/2), n=0..100)]):
L[2..-1]-L[1..-2]; # Robert Israel, Feb 04 2018

Mathematica

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

Crossrefs

Cf. A105148.

Sequence in context: A001227 A369466 A060764 * A355748 A295894 A068307

Adjacent sequences: A105146 A105147 A105148 * A105150 A105151 A105152

Keyword

easy,nonn

Author

Giovanni Teofilatto, Apr 10 2005

Extensions

Edited and extended by Ray Chandler, Apr 16 2005

Status

approved