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A134034
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Number of primes between n^K and (n+1)^K, where K is 1.647862393566467... and n is an integer greater than 0.
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3
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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; internal format)
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OFFSET
| 1,1
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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 (noe(AT)sspectra.com), Sep 04 2008]
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MATHEMATICA
| k=1.647862393566467; Table[Length[Select[Range[Ceiling[n^k], Floor[(n+1)^k]], PrimeQ]], {n, 150}] [From T. D. Noe (noe(AT)sspectra.com), Sep 04 2008]
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CROSSREFS
| Cf. A014085, A060715.
Sequence in context: A154351 A112753 A023589 * A174886 A157415 A154325
Adjacent sequences: A134031 A134032 A134033 * A134035 A134036 A134037
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KEYWORD
| nonn
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AUTHOR
| Dmitry Kamenetsky (Dmitry.Kamenetsky(AT)rsise.anu.edu.au), Jan 11 2008
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Sep 04 2008
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