A225137 - OEIS

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

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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