A225160 Denominators of the sequence 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, 57, 3697, 15302113, 258902783918017, 73384158961115901868286873473, 5848244449673109813614947741525727934929692392922517757697

Offset

1,2

Comments

Numerators of the sequence of fractions f(n) is A165426(n+1), hence sum(A165426(i+1)/a(i),i=1..n) = product(A165426(i+1)/a(i),i=1..n) = A165426(n+2)/A225167(n) = A167182(n+2)/A225167(n).

Links

Table of n, a(n) for n=1..8.

Formula

a(n) = 8^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.

a(n) = 8^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.

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; ...

Maple

b:=n->8^(2^(n-2)); # n > 1
b(1):=8;
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);

Crossrefs

Cf. A100441, A165426, A167182, A225167.

Sequence in context: A289876 A290847 A324420 * A219974 A266051 A202975

Adjacent sequences: A225157 A225158 A225159 * A225161 A225162 A225163

Keyword

nonn

Author

Martin Renner, Apr 30 2013

Status

approved