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A134034
Number of primes between n^K and (n+1)^K, where K is 1.647862393566467... and n is an integer greater than 0.
3
2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 3, 3, 1, 3, 1, 2, 3, 2, 4, 1, 2, 4, 1, 4, 3, 1, 4, 1, 3, 2, 4, 3, 1, 4, 3, 4, 3, 3, 2, 2, 3, 3, 4, 3, 4, 3, 4, 2, 3, 4, 3, 2, 5, 2, 4, 4, 3, 3, 4, 3, 5, 3, 5, 4, 4, 1, 4, 4, 4, 3, 4, 6, 3, 2, 2, 3, 7, 3, 6, 2, 5, 4, 7, 2, 3, 5, 5, 3, 4, 3, 5, 4, 3, 3, 6, 5, 3, 5, 6, 3
OFFSET
1,1
COMMENTS
K is the smallest number such that there is always at least one prime between n^K and (n+1)^K for any integer n>0.
This is not the smallest K. See A143898. [T. D. Noe, Sep 04 2008]
MATHEMATICA
k=1.647862393566467; Table[Length[Select[Range[Ceiling[n^k], Floor[(n+1)^k]], PrimeQ]], {n, 150}] (* T. D. Noe, Sep 04 2008 *)
CROSSREFS
Sequence in context: A112753 A281007 A023589 * A174886 A157415 A154325
KEYWORD
nonn
AUTHOR
Dmitry Kamenetsky, Jan 11 2008
EXTENSIONS
Corrected by T. D. Noe, Sep 04 2008
STATUS
approved