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Search: id:A096954
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| A096954 |
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From Machin's formula: rational approximation for Pi/4=.78539816339744830962... |
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+0
2
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| 951, 1339849258, 9569810428334921, 19132121777295048135244, 81963468350564671450762204559, 1287504688596138051498743351405666674, 23901655485793371607250742363386659018053931
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Machin's formula: Pi/4 = 4*arctan(1/5) - arctan(1/239).
Denominators are given in A096955.
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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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Machin's formula from Mathworld.
W. Lang, more comments.
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FORMULA
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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).
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EXAMPLE
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a(2)/A096955(2) = 9569810428334921/12184551018734375 = .78540...
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CROSSREFS
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Sequence in context: A093247 A020366 A108896 this_sequence A048267 A073500 A121969
Adjacent sequences: A096951 A096952 A096953 this_sequence A096955 A096956 A096957
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jul 23 2004
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