

A225159


Denominators of the sequence of fractions f(n) defined recursively by f(1) = 7/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.


1




OFFSET

1,2


COMMENTS

Numerators of the sequence of fractions f(n) is A165425(n+1), hence sum(A165425(i+1)/a(i),i=1..n) = product(A165425(i+1)/a(i),i=1..n) = A165425(n+2)/A225166(n).


LINKS

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


FORMULA

a(n) = 7^(2^(n2))  product(a(i),i=1..n1), n > 1 and a(1) = 1.
a(n) = 7^(2^(n2))  p(n) with a(1) = 1 and p(n) = p(n1)*a(n1) with p(1) = 1.


EXAMPLE

f(n) = 7, 7/6, 49/43, 2401/2143, ...
7 + 7/6 = 7 * 7/6 = 49/6; 7 + 7/6 + 49/43 = 7 * 7/6 * 49/43 = 2401/258; ...


MAPLE

b:=n>7^(2^(n2)); # n > 1
b(1):=7;
p:=proc(n) option remember; p(n1)*a(n1); 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, A165425, A225166.
Sequence in context: A159604 A090338 A090339 * A078810 A114074 A075337
Adjacent sequences: A225156 A225157 A225158 * A225160 A225161 A225162


KEYWORD

nonn


AUTHOR

Martin Renner, Apr 30 2013


STATUS

approved



