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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).

4, 25, 168, 1228, 9592, 78529, 664614, 5761262, 50847534, 455065829, 4118207819, 37608740621, 346064579205, 3204855540243, 29843276960952, 279224843911465, 2623449162422369, 24739367527714285, 234057667278287556, 2220873676061063755, 21128166733321191012, 201476680593923088240, 1925375268308311490310, 18435220201892878915418

This sequence gives a very good approximation of pi(10^n) (A006880); see (A225138).

a(n)= round(4*((Sum_{i=0..2} (C(i)*(log(log(A*(B+n^(8/3)))))^(2i)))^(n-1))).

Cf. A006880, A225138.

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allocated for Vladimir PletserInteger 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)

4, 25, 168, 1228, 9592, 78529, 664614, 5761262, 50847534, 455065829, 4118207819, 37608740621, 346064579205, 3204855540243, 29843276960952, 279224843911465, 2623449162422369, 24739367527714285, 234057667278287556, 2220873676061063755, 21128166733321191012, 201476680593923088240, 1925375268308311490310, 18435220201892878915418

1,1

Coefficients are A= 3.8055077992656e+14, B= 23.633281628346, C(0)=-196.69026129533, C(1)=27.625972037921, C(2)=-0.92494798392435.

This sequence gives a very good approximation of pi(10^n) (A006880); see (A225138)

Vladimir Pletser, <a href="/A225137/b225137.txt">Table of n, a(n) for n = 1..500</a>

a(n)= round(4*((Sum_{i=0..2} (C(i)*(log(log(A*(B+n^(8/3)))))^(2i)))^(n-1)))

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);

Cf. A006880, A225138

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Vladimir Pletser, Apr 29 2013

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allocated for Vladimir Pletser

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