%I #14 Jun 14 2024 08:47:17

%S 2,2,7,14,37,100,271,742,2054,5813,16507,47501,137306,399685,1169789,

%T 3438915,10153559,30083443,89426830,266598341,796863253,2387439540,

%U 7168302094,21565117858,64993345011,196202749033,593205591259,1796057856430,5445108651668,16528162238845

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

%H Amiram Eldar, <a href="/A061274/b061274.txt">Table of n, a(n) for n = 1..52</a> (calculated from the b-file at A071973)

%F a(n) = A071973(n) - A071973(n-1). - _Amiram Eldar_, Jun 14 2024

%e 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...

%p See A061273.

%t p = q = 0; Do[m = n; q = PrimePi[Pi^n]; Print[q - p]; p = q, {n, 1, 28}]

%t Differences[PrimePi[Pi^Range[0,27]]] (* _Harvey P. Dale_, Aug 17 2016 *)

%Y Cf. A061273, A071973.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Apr 25 2001

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

%E Edited and extended by _Robert G. Wilson v_, Jun 18 2002

%E a(28)-a(30) from _Amiram Eldar_, Jun 14 2024