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A192227
Number of primes in the range (n - 2*sqrt(sqrt(n)), n].
1
0, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1
OFFSET
1,3
COMMENTS
a(n) is probably positive for all n > 191913030. - Charles R Greathouse IV, Jul 01 2011
FORMULA
Conjecturally, a(n) ~ 2*n^(1/4)/log n. - Charles R Greathouse IV, Jul 01 2011
MAPLE
A192227 := proc(n) local nhi, nlo ; nhi := n ; nlo := floor( n-2*root[4](n)) ; numtheory[pi](nhi)-numtheory[pi](nlo) ; end proc; # R. J. Mathar, Jul 12 2011
MATHEMATICA
Table[PrimePi[n]-PrimePi[n-2*Sqrt[Sqrt[n]]], {n, 90}] (* Harvey P. Dale, Feb 24 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved