A137379 Number of primes between (n + 1)^Pi and n^Pi.

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

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2008

Keywords

• nonn
• easy

Examples

			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..);
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Programs

Maple

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

Mathematica

Table[PrimePi[(n + 1)^Pi] - PrimePi[n^Pi], {n, 0, 29}]
Differences[PrimePi[Range[0,60]^Pi]] (* Harvey P. Dale, Aug 17 2024 *)

Formula

a(n) = A000720(A061294(n+1)) - A000720(A061294(n)). - R. J. Mathar, Apr 16 2008

Extensions

More terms from R. J. Mathar, Apr 16 2008