A096955 Denominators of rational approximation to Pi/4 from Machins's formula.

1195, 1706489875, 12184551018734375, 24359780855939418203125, 104359128170408663038552734375, 1639301884061026141391921953564453125, 30432532948821209122295591520605416259765625

Offset: 0

Author

Wolfdieter Lang, Jul 23 2004

Keywords

• nonn
• frac
• easy

Comments

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

Numerators are given in A096954.

Examples

			A096954(7)/a(7) =
170660807873601670198453967268421248219727522686104 /217292089321202035784330810406062747771759033203125
= 0.78539816339715...
		

References

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

Links

• Wolfdieter Lang, More comments.
• Eric Weisstein's World of Mathematics, Machin's Formula.

Crossrefs

Cf. A003881, A096954.

Formula

a(n) = denominator(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).