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A225157
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Denominators of the sequence of fractions f(n) defined recursively by f(1) = 5/1; 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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1, 4, 21, 541, 345181, 136901485261, 21135572172649245550621, 496712610012943408146407697714437299262548141, 271328559212953102170688304392824035451911661168940831351173011072850527195615099225368381
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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) = 5^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.
a(n) = 5^(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) = 5, 5/4, 25/21, 625/541, ...
5 + 5/4 = 5 * 5/4 = 25/4; 5 + 5/4 + 25/21 = 5 * 5/4 * 25/21 = 625/84; ...
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MAPLE
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b:=n->5^(2^(n-2)); # n > 1
b(1):=5;
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,frac
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AUTHOR
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STATUS
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approved
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