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Search: id:A137379
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| A137379 |
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Number of primes between (n + 1)^Pi and n^Pi. |
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+0
1
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| 0, 4, 7, 10, 15, 23, 28, 37, 43, 54, 64, 78, 83, 103, 113, 128, 145, 159, 180, 186, 215, 237, 244, 277, 296, 313, 340, 369, 384, 417, 430, 472, 504, 515, 550, 590, 620, 641, 686, 706, 746, 789, 812, 857, 902, 918, 964, 1016, 1043, 1095, 1149, 1158, 1213, 1276
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = A000720(A061294(n+1))-A000720(A061294(n)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2008
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EXAMPLE
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0 primes between: 0^Pi and 1^Pi (between: 0 and 1);
4 primes between: 1^Pi and 2^Pi (between: 1 and 8.82..);
7 primes between: 2^Pi and 3^Pi (between: 8.82.. and 31.54..);
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MAPLE
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Digits := 30 : A000720 := proc(n) numtheory[pi](n) ; end: A061294 := proc(n) floor(n^Pi) ; end: A137379 := proc(n) A000720(A061294(n+1))-A000720(A061294(n)) ; end: seq(A137379(n), n=0..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2008
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MATHEMATICA
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Table[PrimePi[(n + 1)^Pi] - PrimePi[n^Pi], {n, 0, 29}]
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CROSSREFS
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Sequence in context: A095875 A071408 A137461 this_sequence A096676 A092863 A138694
Adjacent sequences: A137376 A137377 A137378 this_sequence A137380 A137381 A137382
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 09 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2008
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