login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A096955 From Machin's formula: rational approximation for Pi/4 = 0.78539816339744... = A003881. 3
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

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

Machin's formula from Mathworld.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 22:18 EDT 2019. Contains 325269 sequences. (Running on oeis4.)