A137379 - OEIS

%I #12 Aug 17 2024 13:03:30

%S 0,4,7,10,15,23,28,37,43,54,64,78,83,103,113,128,145,159,180,186,215,

%T 237,244,277,296,313,340,369,384,417,430,472,504,515,550,590,620,641,

%U 686,706,746,789,812,857,902,918,964,1016,1043,1095,1149,1158,1213,1276

%N Number of primes between (n + 1)^Pi and n^Pi.

%H Vincenzo Librandi, <a href="/A137379/b137379.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A000720(A061294(n+1)) - A000720(A061294(n)). - _R. J. Mathar_, Apr 16 2008

%e 0 primes between: 0^Pi and 1^Pi (between: 0 and 1);

%e 4 primes between: 1^Pi and 2^Pi (between: 1 and 8.82..);

%e 7 primes between: 2^Pi and 3^Pi (between: 8.82.. and 31.54..);

%p 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_, Apr 16 2008

%t Table[PrimePi[(n + 1)^Pi] - PrimePi[n^Pi], {n, 0, 29}]

%t Differences[PrimePi[Range[0,60]^Pi]] (* _Harvey P. Dale_, Aug 17 2024 *)

%K nonn,easy

%O 0,2

%A _Vladimir Joseph Stephan Orlovsky_, Apr 09 2008

%E More terms from _R. J. Mathar_, Apr 16 2008