A096954 Numerators of rational approximation to Pi/4 from Machins's formula.

951, 1339849258, 9569810428334921, 19132121777295048135244, 81963468350564671450762204559, 1287504688596138051498743351405666674, 23901655485793371607250742363386659018053931

Offset

0,1

Comments

Machin's formula: Pi/4 = 4*arctan(1/5) - arctan(1/239).

Denominators are given in A096955.

References

W. Walter, Analysis I (in German), Springer, 3. Auflage, 1992; p. 216.

Links

Table of n, a(n) for n=0..6.

Wolfdieter Lang, More comments.

Eric Weisstein's World of Mathematics, Machin's Formula.

Formula

a(n)=numerator(M(n)), with M(n)=4*arctan(1/5, n) - arctan(1/239, n) with arctan(x, n):=sum((((-1)^k)*x^(2k+1))/(2*k+1), k=0..n).

Example

a(2)/A096955(2) = 9569810428334921/12184551018734375 = .78540...

Crossrefs

Cf. A003881, A096955.

Sequence in context: A108896 A260174 A285157 * A048267 A251677 A073500

Adjacent sequences: A096951 A096952 A096953 * A096955 A096956 A096957

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Jul 23 2004

Status

approved