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A096955
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From Machin's formula: rational approximation for Pi/4 = 0.78539816339744... = A003881.
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5
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1195, 1706489875, 12184551018734375, 24359780855939418203125, 104359128170408663038552734375, 1639301884061026141391921953564453125, 30432532948821209122295591520605416259765625
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OFFSET
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0,1
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COMMENTS
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Machin's formula: Pi/4 = 4*arctan(1/5) - arctan(1/239).
Numerators are given in A096954.
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REFERENCES
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W. Walter, Analysis I (in German), Springer, 3. Auflage, 1992; p. 216.
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LINKS
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Table of n, a(n) for n=0..6.
Machin's formula from Mathworld.
W. Lang, more comments.
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FORMULA
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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).
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EXAMPLE
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A096954(7)/a(7) =
170660807873601670198453967268421248219727522686104 /217292089321202035784330810406062747771759033203125
= 0.78539816339715...
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CROSSREFS
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Sequence in context: A251916 A251915 A166221 * A113898 A059401 A059402
Adjacent sequences: A096952 A096953 A096954 * A096956 A096957 A096958
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang, Jul 23 2004
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STATUS
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approved
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