A134034 Number of primes between n^K and (n+1)^K, where K is 1.647862393566467... and n is an integer greater than 0.

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

Author

Dmitry Kamenetsky, Jan 11 2008

Keywords

• nonn

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]

Crossrefs

Cf. A014085, A060715.

Programs

Mathematica

k=1.647862393566467; Table[Length[Select[Range[Ceiling[n^k],Floor[(n+1)^k]], PrimeQ]], {n,150}] (* T. D. Noe, Sep 04 2008 *)

Extensions

Corrected by T. D. Noe, Sep 04 2008