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Search: id:A156736
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| A156736 |
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Signed greedy Egyptian fraction for Pi/2 |
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+0
2
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| 1, 2, 14, -1582, -7497258, 303297921775458, -2646995089135122277190614296178, 82888930564911423983289917045230098319343306166666586941750246
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The second and fourth convergents of Pi (22/7 and 355/113) appear when truncating the series to three and four terms.
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LINKS
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Wikipedia, Greedy algorithm for Egyptian fractions
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FORMULA
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Sum(n>=0,1/a(n))=Pi/2
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EXAMPLE
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1+1/2+1/14=11/7=(1/2)(22/7)
1+1/2+1/14-1/1582=355/226=(1/2)(355/113)
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PROGRAM
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(PARI) x=Pi/2; for (k=0, 7, d=round(1/x); x=x-1/d; print1(d, ", "))
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CROSSREFS
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Cf. A001466, A156269, A156618.
Cf. A156750. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 03 2009]
Sequence in context: A144017 A032419 A130421 this_sequence A006266 A106484 A027739
Adjacent sequences: A156733 A156734 A156735 this_sequence A156737 A156738 A156739
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KEYWORD
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sign
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AUTHOR
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Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Feb 14 2009
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