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A225169
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Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 10/1; 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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3
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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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FORMULA
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a(n) = 10^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/10.
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EXAMPLE
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f(n) = 10, 10/9, 100/91, 10000/9181, ...
10 + 10/9 = 10 * 10/9 = 100/9; 10 + 10/9 + 100/91 = 10 * 10/9 * 100/91 = 10000/819; ...
s(n) = 1/b(n) = 10, 100/9, 10000/819, ...
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MAPLE
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b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:
b(1):=1/10;
a:=n->10^(2^(n-1))*b(n);
seq(a(i), i=1..7);
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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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