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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

Table of n, a(n) for n=0..6.

Machin's formula from Mathworld.

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.)