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%I #7 Apr 30 2013 12:29:40
%S 4,25,168,1228,9592,78529,664614,5761262,50847534,455065829,
%T 4118207819,37608740621,346064579205,3204855540243,29843276960952,
%U 279224843911465,2623449162422369,24739367527714285,234057667278287556,2220873676061063755
%N Integer nearest to (4*((S(n))^(n-1))), where S(n) = Sum_{i=0..2} (C(i)*(log(log(A*(B+n^(8/3)))))^(2i)) (see coefficients A, B, C(i) in comments).
%C Coefficients are A= 3.8055077992656e+14, B= 23.633281628346, C(0)=-196.69026129533, C(1)=27.625972037921, C(2)=-0.92494798392435.
%C This sequence gives a very good approximation of pi(10^n) (A006880); see (A225138).
%H Vladimir Pletser, <a href="/A225137/b225137.txt">Table of n, a(n) for n = 1..500</a>
%F a(n)= round(4*((Sum_{i=0..2} (C(i)*(log(log(A*(B+n^(8/3)))))^(2i)))^(n-1))).
%p A:= 3.8055077992656e+14: B:= 23.633281628346: C(0):= -196.69026129533: C(1):=27.625972037921: C(2):= -0.92494798392435: b:=n->log(log(A*(B+n^(8/3)))): c:=n->sum(C(i)*(b(n))^(2*i), i=0..2): seq(round(4*(c(n))^(n-1)), n=1..24);
%Y Cf. A006880, A225138.
%K nonn
%O 1,1
%A _Vladimir Pletser_, Apr 29 2013
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