Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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