A188817 Number of primes between n-sqrt(n) and n+sqrt(n), inclusive.

1, 2, 2, 3, 3, 2, 2, 1, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 2, 2, 1, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 2, 3, 4, 3, 3, 3, 4, 4, 4, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 5, 5, 5, 4, 4, 3, 4, 4, 4, 4, 5, 4, 4, 4, 4, 3, 4, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 4, 3, 3, 3, 4, 3, 3, 2

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 11 2011

Keywords

• nonn
• look

Comments

It appears that all terms are positive.

Examples

			a(1)=1 because prime 2 is in [0,2].
a(2)=2 because primes 2 and 3 are between 2-sqrt(2) and 2+sqrt(2).
a(3)=2 because primes 2 and 3 are between 3-sqrt(3) and 3+sqrt(3).
a(4)=3 because primes 2, 3, and 5 are in [2,6].
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A114021, A060715.

Programs

Maple

A188817 := proc(n) local low,hi; low := n-sqrt(n) ; if not issqr(n) then low := ceil(low) ; end if; hi := n+sqrt(n) ; if not issqr(n) then hi := floor(hi) ; end if; numtheory[pi](hi)-numtheory[pi](low-1) ; end proc:
seq(A188817(n),n=1..50) ; # R. J. Mathar, Apr 12 2011

Mathematica

Join[{1, 2, 2, 3}, Table[PrimePi[n + Sqrt[n]] - PrimePi[n - Sqrt[n]], {n, 5, 120}]] (* T. D. Noe, Apr 11 2011 *)

Extensions

Corrected by T. D. Noe, Apr 11 2011