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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 (list; graph; refs; listen; history; text; internal format)
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. [From 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}] [From 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

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Last modified May 25 13:44 EDT 2022. Contains 354071 sequences. (Running on oeis4.)