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 A096954 From Machin's formula: rational approximation for Pi/4=.78539816339744830962... 5
 951, 1339849258, 9569810428334921, 19132121777295048135244, 81963468350564671450762204559, 1287504688596138051498743351405666674, 23901655485793371607250742363386659018053931 (list; graph; refs; listen; history; text; internal format)
 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 W. Lang, more comments. 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 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

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Last modified July 19 12:49 EDT 2019. Contains 325159 sequences. (Running on oeis4.)