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A188817
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Number of primes between n-sqrt(n) and n+sqrt(n), inclusive.
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7
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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
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OFFSET
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1,2
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COMMENTS
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It appears that all terms are positive.
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LINKS
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EXAMPLE
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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].
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MAPLE
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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:
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MATHEMATICA
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Join[{1, 2, 2, 3}, Table[PrimePi[n + Sqrt[n]] - PrimePi[n - Sqrt[n]], {n, 5, 120}]] (* T. D. Noe, Apr 11 2011 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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