A061274 Number of primes between Pi^(n-1) and Pi^n.

2, 2, 7, 14, 37, 100, 271, 742, 2054, 5813, 16507, 47501, 137306, 399685, 1169789, 3438915, 10153559, 30083443, 89426830, 266598341, 796863253, 2387439540, 7168302094, 21565117858, 64993345011, 196202749033, 593205591259, 1796057856430, 5445108651668, 16528162238845

Offset: 1

Author

Amarnath Murthy, Apr 25 2001

Keywords

• nonn

Examples

			a(1) = 2 as 2 and 3 are the two primes between 1 and Pi. a(4) = 14 as there are 14 primes between Pi^3 = 31.006... and Pi^4 = 97.409091...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..52 (calculated from the b-file at A071973)

Crossrefs

Cf. A061273, A071973.

Programs

Maple

See A061273.

Mathematica

p = q = 0; Do[m = n; q = PrimePi[Pi^n]; Print[q - p]; p = q, {n, 1, 28}]
Differences[PrimePi[Pi^Range[0,27]]] (* Harvey P. Dale, Aug 17 2016 *)

Formula

a(n) = A071973(n) - A071973(n-1). - Amiram Eldar, Jun 14 2024

Extensions

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), May 17 2001

Edited and extended by Robert G. Wilson v, Jun 18 2002

a(28)-a(30) from Amiram Eldar, Jun 14 2024