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A225167 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 8/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. 1

%I #5 May 01 2013 12:23:54

%S 1,7,399,1475103,22572192792639,5844003553148435725257076863,

%T 428857285713570950220841681681938481172663051541516755199

%N Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 8/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

%C Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165426(n+2), hence sum(A165426(i+1)/A225160(i),i=1..n) = product(A165426(i+1)/A225160(i),i=1..n) = A165426(n+2)/a(n) = A167182(n+2)/a(n).

%F a(n) = 8^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/8.

%e f(n) = 8, 8/7, 64/57, 4096/3697, ...

%e 8 + 8/7 = 8 * 8/7 = 64/7; 8 + 8/7 + 64/57 = 8 * 8/7 * 64/57 = 4096/399; ...

%e s(n) = 1/b(n) = 8, 64/7, 4096/399, ...

%p b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:

%p b(1):=1/8;

%p a:=n->8^(2^(n-1))*b(n);

%p seq(a(i),i=1..8);

%Y Cf. A076628, A165426, A167182, A225160.

%K nonn

%O 1,2

%A _Martin Renner_, Apr 30 2013

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)