OFFSET
1,2
COMMENTS
There is an asymptotic formula for this sequence (see formula line).
LINKS
FORMULA
a(n) = n*(sqrt(2*n/3)-1/5) + O(sqrt(n)) and this is sharp (see link).
EXAMPLE
We have a(7)=17 and the continued fraction for a(7) + 8^2/a(7) is [20, 1, 3, 4], hence a(8)=20.
MATHEMATICA
a = {1}; Do[AppendTo[a, Max@ ContinuedFraction[a[[n - 1]] + (n^2)/a[[n - 1]]]], {n, 2, 100}]; a (* Michael De Vlieger, Sep 14 2015 *)
PROG
(PARI) a=1; for(n=2, 100, a=vecmax(contfrac(a+n^2/a)); print1(a, ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Sep 13 2015
STATUS
approved