cp's OEIS Frontend

A306604 Number of perfect squares in the half-open interval [Pi^(n-1), Pi^n).

%I A306604 #22 Mar 01 2019 16:26:39
%S A306604 0,1,2,2,4,8,14,23,43,75,134,236,419,743,1316,2333,4135,7329,12992,
%T A306604 23026,40813,72338,128218,227259,402806,713955,1265453,2242956,
%U A306604 3975538,7046456,12489518,22137096,39236979,69545736,123266607,218484372,387253468,686388899
%N A306604 Number of perfect squares in the half-open interval [Pi^(n-1), Pi^n).
%C A306604 Inspired by A306486.
%H A306604 Alois P. Heinz, <a href="/A306604/b306604.txt">Table of n, a(n) for n = 0..4024</a>
%F A306604 a(n) = ceiling(Pi^(n/2)) - ceiling(Pi^((n-1)/2)).
%F A306604 a(n) = A102477(n) - A102477(n-1).
%F A306604 Sum_{i=0..n} a(i) = A102475(n) for n > 0.
%F A306604 Lim_{n->oo} a(n+1)/a(n) = sqrt(Pi) = 1.7724538509... = A002161.
%e A306604 a(4) = 4: in the interval [Pi^3, Pi^4) = [31.006..., 97.409...) = are four perfect squares: 36, 49, 64, 81.
%p A306604 a:= n-> (f-> f(n)-f(n-1))(i-> ceil(Pi^(i/2))):
%p A306604 seq(a(n), n=0..42);
%Y A306604 Cf. A000290, A000796, A002161, A091925, A092425, A102475, A102477, A306486.
%K A306604 nonn
%O A306604 0,3
%A A306604 _Alois P. Heinz_, Feb 27 2019