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A089616
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Number of primes between n^2 and (n+1/6)^2.
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1
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0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 2, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 2, 2, 3, 1, 2, 4, 2, 3, 2, 4, 1, 1, 1, 1, 3, 2, 2, 2, 2, 1, 2, 4, 1, 2, 2, 1, 4, 2, 2, 3, 3, 4, 1, 2, 4, 3, 2, 3, 1, 3, 2, 2, 3, 3, 3, 4, 2, 3, 3, 1, 5, 2, 3, 3, 5, 2, 5, 3, 4, 4, 5, 1, 3, 6, 4, 4, 7, 5, 5, 2, 2, 3, 4, 3, 4
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OFFSET
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1,10
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LINKS
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MAPLE
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seq(numtheory:-pi(floor((n+1/6)^2))-numtheory:-pi(n^2), n=1..200); # Robert Israel, Jan 02 2018
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MATHEMATICA
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Table[PrimePi[(n+1/6)^2]-PrimePi[n^2], {n, 110}] (* Harvey P. Dale, Sep 17 2013 *)
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PROG
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(PARI) pbetweensq2(n) = { for(x=1, n, c=0; for(y=floor(x)^2, (x+1/6)^2, if(isprime(y), c++) ); print1(c", ") ) }
(PARI) a(n) = primepi((n+1/6)^2) - primepi(n^2); \\ Michel Marcus, Jan 03 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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