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%I #17 Mar 04 2020 13:48:47
%S 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,
%T 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,
%U 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
%N Number of primes between n-sqrt(n) and n+sqrt(n), inclusive.
%C It appears that all terms are positive.
%H Robert Israel, <a href="/A188817/b188817.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=1 because prime 2 is in [0,2].
%e a(2)=2 because primes 2 and 3 are between 2-sqrt(2) and 2+sqrt(2).
%e a(3)=2 because primes 2 and 3 are between 3-sqrt(3) and 3+sqrt(3).
%e a(4)=3 because primes 2, 3, and 5 are in [2,6].
%p 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:
%p seq(A188817(n),n=1..50) ; # _R. J. Mathar_, Apr 12 2011
%t Join[{1, 2, 2, 3}, Table[PrimePi[n + Sqrt[n]] - PrimePi[n - Sqrt[n]], {n, 5, 120}]] (* _T. D. Noe_, Apr 11 2011 *)
%Y Cf. A114021, A060715.
%K nonn,look
%O 1,2
%A _Juri-Stepan Gerasimov_, Apr 11 2011
%E Corrected by _T. D. Noe_, Apr 11 2011
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