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

1,1

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]

Links

Table of n, a(n) for n=1..105.

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

Cf. A014085, A060715.

Sequence in context: A112753 A281007 A023589 * A174886 A157415 A154325

Adjacent sequences: A134031 A134032 A134033 * A134035 A134036 A134037

Keyword

nonn

Author

Dmitry Kamenetsky, Jan 11 2008

Extensions

Corrected by T. D. Noe, Sep 04 2008

Status

approved