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, 7, 399, 1475103, 22572192792639, 5844003553148435725257076863, 428857285713570950220841681681938481172663051541516755199

Offset

1,2

Comments

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).

Links

Table of n, a(n) for n=1..7.

Formula

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

Example

f(n) = 8, 8/7, 64/57, 4096/3697, ...
8 + 8/7 = 8 * 8/7 = 64/7; 8 + 8/7 + 64/57 = 8 * 8/7 * 64/57 = 4096/399; ...
s(n) = 1/b(n) = 8, 64/7, 4096/399, ...

Maple

b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:
b(1):=1/8;
a:=n->8^(2^(n-1))*b(n);
seq(a(i), i=1..8);

Crossrefs

Cf. A076628, A165426, A167182, A225160.

Sequence in context: A042527 A203588 A015022 * A160292 A215562 A099125

Adjacent sequences: A225164 A225165 A225166 * A225168 A225169 A225170

Keyword

nonn

Author

Martin Renner, Apr 30 2013

Status

approved