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

1,1

Links

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

Formula

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

Example

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...

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 *)

Crossrefs

Cf. A061273, A071973.

Sequence in context: A298959 A162460 A187306 * A061575 A306009 A290646

Adjacent sequences: A061271 A061272 A061273 * A061275 A061276 A061277

Keyword

nonn

Author

Amarnath Murthy, Apr 25 2001

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

Status

approved