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A096955
Denominators of rational approximation to Pi/4 from Machins's formula.
5
1195, 1706489875, 12184551018734375, 24359780855939418203125, 104359128170408663038552734375, 1639301884061026141391921953564453125, 30432532948821209122295591520605416259765625
OFFSET
0,1
COMMENTS
Machin's formula: Pi/4 = 4*arctan(1/5) - arctan(1/239).
Numerators are given in A096954.
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.
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).
EXAMPLE
A096954(7)/a(7) =
170660807873601670198453967268421248219727522686104 /217292089321202035784330810406062747771759033203125
= 0.78539816339715...
CROSSREFS
Sequence in context: A251916 A251915 A166221 * A113898 A059401 A059402
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Jul 23 2004
STATUS
approved