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Search: id:A063673
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| A063673 |
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Denominators of sequence {3/1, 13/4, 16/5, 19/6, 22/7, 179/57, 201/64, 223/71, 245/78, 267/85, 289/92, 311/99, 333/106, ... } of approximations to Pi with increasing denominators, where each approximation is an improvement on its predecessors. |
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+0
2
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| 1, 4, 5, 6, 7, 57, 64, 71, 78, 85, 92, 99, 106, 113, 16604, 16717, 16830, 16943, 17056, 17169, 17282, 17395, 17508, 17621, 17734, 17847, 17960, 18073, 18186, 18299, 18412, 18525, 18638, 18751
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The fraction 355/113 is so accurate that improves the approximation of Pi by five significant digits over the previous (333/106). To find a slightly more accurate approximation we have to go to 52163 / 16604. - Sergio Pimentel (ferdiego(AT)cox-internet.com), Sep 13 2005
Pi = 3.1415926.... is an irrational number, and can't be exactly represented by a fraction with rational numerator and denominators. - Sergio Pimentel (ferdiego(AT)cox-internet.com), Sep 13 2005
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EXAMPLE
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333/106 = 3.1415094... is 99.99% accurate
355/113 = 3.1415929... is 99.99999% accurate
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PROGRAM
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(PARI) A063673(limit) = { local(best, tmp); best=Pi-3; for(n=1, limit, tmp=abs(round(Pi*n)/n-Pi); if(tmp<best, best=tmp; print1(n", ") ) ) } - Charles R. Greathouse IV, Aug 23 2006
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CROSSREFS
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A063674.
Adjacent sequences: A063670 A063671 A063672 this_sequence A063674 A063675 A063676
Sequence in context: A071177 A010754 A051036 this_sequence A105737 A033597 A088720
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KEYWORD
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frac,nonn
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AUTHOR
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Suren L. Fernando (fernando(AT)truman.edu), Jul 27 2001
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EXTENSIONS
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3 more terms from Sergio Pimentel (ferdiego(AT)cox-internet.com), Sep 13 2005
More terms from Charles R. Greathouse IV, Aug 23 2006
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