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A225159
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Denominators of the sequence of fractions f(n) defined recursively by f(1) = 7/1; 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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FORMULA
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a(n) = 7^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.
a(n) = 7^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.
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EXAMPLE
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f(n) = 7, 7/6, 49/43, 2401/2143, ...
7 + 7/6 = 7 * 7/6 = 49/6; 7 + 7/6 + 49/43 = 7 * 7/6 * 49/43 = 2401/258; ...
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MAPLE
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b:=n->7^(2^(n-2)); # n > 1
b(1):=7;
p:=proc(n) option remember; p(n-1)*a(n-1); end;
p(1):=1;
a:=proc(n) option remember; b(n)-p(n); end;
a(1):=1;
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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