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 A096955 From Machin's formula: rational approximation for Pi/4 = 0.78539816339744... = A003881. 5
 1195, 1706489875, 12184551018734375, 24359780855939418203125, 104359128170408663038552734375, 1639301884061026141391921953564453125, 30432532948821209122295591520605416259765625 (list; graph; refs; listen; history; text; internal format)
 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 W. Lang, more comments. 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 Adjacent sequences:  A096952 A096953 A096954 * A096956 A096957 A096958 KEYWORD nonn,frac,easy AUTHOR Wolfdieter Lang, Jul 23 2004 STATUS approved

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Last modified August 12 15:13 EDT 2022. Contains 356077 sequences. (Running on oeis4.)