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A225163
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Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 3/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.
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2
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OFFSET
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1,2
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COMMENTS
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LINKS
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Paul Yiu, Recreational Mathematics, Department of Mathematics, Florida Atlantic University, 2003, Chapter 5.4, p. 207 (Project).
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FORMULA
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a(n) = 3^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/3.
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EXAMPLE
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f(n) = 3, 3/2, 9/7, 81/67, ...
3 + 3/2 = 3 * 3/2 = 9/2; 3 + 3/2 + 9/7 = 3 * 3/2 * 9/7 = 81/14; ...
s(n) = 1/b(n) = 3, 9/2, 81/14, ...
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MAPLE
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b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:
b(1):=1/3;
a:=n->3^(2^(n-1))*b(n);
seq(a(i), i=1..9);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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