

A188817


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


7



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

It appears that all terms are positive.


LINKS

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


EXAMPLE

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


MAPLE

A188817 := proc(n) local low, hi; low := nsqrt(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](low1) ; 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 *)


CROSSREFS

Cf. A114021, A060715.
Sequence in context: A220517 A271076 A087175 * A271099 A165299 A071820
Adjacent sequences: A188814 A188815 A188816 * A188818 A188819 A188820


KEYWORD

nonn,look


AUTHOR

JuriStepan Gerasimov, Apr 11 2011


EXTENSIONS

Corrected by T. D. Noe, Apr 11 2011


STATUS

approved



