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Search: id:A113479
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| A113479 |
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Starting with the fraction 4/1 as the first term, a(n) is the numerator of the reduced fraction of the n-th term according to the rule: if n is even, multiply the previous term by n/(n+1) otherwise multiply the previous term by (n+1)/n. |
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+0
1
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| 4, 8, 32, 128, 256, 512, 4096, 32768, 65536, 131072, 524288, 2097152, 4194304, 8388608, 134217728, 2147483648, 4294967296, 8589934592, 34359738368, 137438953472, 274877906944, 549755813888, 4398046511104, 35184372088832
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The fractions forming these numerators slowly converge to Pi. The 1000th term at 2000 digits precision yields 3.1400...
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REFERENCES
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John Derbshire, Prime Obsession, 2004, Joseph Henry Press, p. 16.
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EXAMPLE
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The first term is 4/1. then the 2nd term is 4/1*2/(2+1) = 8/3. So 8 is the 2nd entry in the table.
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PROGRAM
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(PARI) g(n) = { a=4; b=1; print1(4", "); for(x=2, n, if(x%2==0, a=a*x; b=b*(x+1), a=a*(x+1); b=b*x); print1(numerator(a/b)", ") ) }
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CROSSREFS
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Adjacent sequences: A113476 A113477 A113478 this_sequence A113480 A113481 A113482
Sequence in context: A094867 A086344 A068205 this_sequence A103970 A034785 A075398
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Jan 09 2006
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