A225137 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

Offset

1,1

Comments

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).

Links

Vladimir Pletser, Table of n, a(n) for n = 1..500

Formula

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

Maple

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);

Crossrefs

Cf. A006880, A225138.

Sequence in context: A128419 A372216 A226945 * A229255 A006880 A227693

Adjacent sequences: A225134 A225135 A225136 * A225138 A225139 A225140

Keyword

nonn

Author

Vladimir Pletser, Apr 29 2013

Status

approved