Revision History for A225156
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| A225156
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Denominators of the sequence 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.
(history;
published version)
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#6 by N. J. A. Sloane at Wed May 01 12:07:16 EDT 2013
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#5 by N. J. A. Sloane at Wed May 01 12:07:03 EDT 2013
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| KEYWORD
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nonn,frac,changed
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| STATUS
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proposed
editing
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Discussion
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| Wed May 01
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| N. J. A. Sloane: added missing keyword
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#4 by Martin Renner at Tue Apr 30 19:09:10 EDT 2013
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#3 by Martin Renner at Tue Apr 30 19:02:47 EDT 2013
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#2 by Martin Renner at Tue Apr 30 17:54:00 EDT 2013
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| NAME
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allocatedDenominators of the sequence 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 forsequence Martinare Rennerequal.
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| DATA
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1, 2, 7, 67, 5623, 37772347, 1653794703916063, 3104205768420613437667191487267, 10767416908549848056705041797805600349527548164015760674541223
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| OFFSET
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1,2
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| COMMENTS
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Numerators of the sequence of fractions f(n) is A165421(n+1), hence sum(A165421(i+1)/a(i),i=1..n) = product(A165421(i+1)/a(i),i=1..n) = A165421(n+2)/A000000(n) = A011764(n-1)/A000000(n).
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| LINKS
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Paul Yiu, <a href="http://math.fau.edu/yiu/RecreationalMathematics2003.pdf">Recreational Mathematics</a>, 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-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.
a(n) = 3^(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) = 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; ...
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| MAPLE
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b:=n->3^(2^(n-2)); # n > 1
b(1):=3;
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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Cf. A011764, A100441, A165421.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Martin Renner, Apr 30 2013
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| STATUS
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approved
editing
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#1 by Martin Renner at Tue Apr 30 17:54:00 EDT 2013
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| NAME
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allocated for Martin Renner
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| KEYWORD
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allocated
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| STATUS
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approved
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