OFFSET
1,2
COMMENTS
Sum_{k>=1} 1/k^2 = zeta(2) = Pi^2/6.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Limit_{n ->infinity} a(n)/n = C =1.6....
EXAMPLE
The simple continued fraction for Sum_{k=1..10} 1/k^2 is [1, 1, 1, 4, 1, 1, 10, 4, 1, 2, 5, 2, 1, 24] which contains 14 terms, hence a(10) = 14.
MATHEMATICA
lcf[f_] := Length[ContinuedFraction[f]]; lcf /@ Accumulate[Table[1/k^2, {k, 1, 100}]] (* Amiram Eldar, Apr 30 2022 *)
PROG
(PARI) for(n=1, 100, print1(length(contfrac(sum(i=1, n, 1/i^2))), ", "))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 18 2002
STATUS
approved