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Search: id:A125889
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| A125889 |
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Denominator of sum of first n ratios of Fibonacci to Lucas numbers. |
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+0
2
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| 2, 1, 3, 6, 42, 462, 1386, 1889118, 17946621, 735811461
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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A125888(n) = numerator(SUM[i=1..n]F(i)/L(i)) = SUM[i=1..n] A000045(i)/A000032(i) = n/sqrt(5) + O(1) (Max A., Dec 7, 2006). denominator(SUM[i=1..n]A000045(i)/A000032(i)). GCD(F(i),L(i)) <= 2, so the ratio reduces when there is a factor of two in common, every third term. Example as continued fraction: 0 + 1+1/3+2/4+3/7+5/11+8/18+13/29+21/47+34/76+55/123 = 1/1+ 1/19+ 1/4+ 1/1+ 1/13+ 1/2+ 1/4+ 1/1+ 1/6+ 1/6+ 1/1+ 1/85+ 1/1+ 1/4+ 1/2.
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FORMULA
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a(n) = denominator(SUM[i=1..n]F(i)/L(i)) = denominator(SUM[i=1..n]A000045(i)/A000032(i)).
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EXAMPLE
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The fractions, reduced to lowest terms, begin:
0/2, 1/1, 4/3, 11/6, 95/42, 1255/462, 4381/1386, 7662223/1889118, 80819870/17946621, 3642636055/735811461, ...
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CROSSREFS
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Cf. A000032, A000045, A125888.
Sequence in context: A024741 A024961 A140644 this_sequence A116381 A073901 A058170
Adjacent sequences: A125886 A125887 A125888 this_sequence A125890 A125891 A125892
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 13 2006
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