|
|
A081088
|
|
Smallest partial quotients of a series of continued fractions that have a sum of unity, where the n-th continued fraction term is [0; a(n),a(n-1),...,a(1)], so that sum(n>0, [0; a(n),a(n-1),...,a(1)] ) = 1, with a(1)=2.
|
|
4
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
a(n+1) appears to be divisible by a(n) for n>0; a(n+1)/a(n) = A081089(n). Also log(a(n+1))/log(a(n)) -> 1+sqrt(2). The 8th term has 79 digits, while the 9th term has 199 digits.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
1 = [0;2] + [0;2,2] + [0;10,2,2] + [0;260,10,2,2] + [0;703300,260,10,2,2] + [0;128651592765800,703300,260,10,2,2] +... = .5 + .4 + .0961538461 + .0038447319 + .0000014218 + ...
|
|
CROSSREFS
|
|
|
KEYWORD
|
cofr,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|