Limit of the ratio of a(n) to a(n-1) in A346526
Statement: , where an = A346526(n) (proposed by Stefano Spezia, Jul 22 2021).
Proof
The sequence is infinite; obviously we have and .
Since , , and are definite terms in the sequence for non-negative integer ; therefore for arbitrary , we have
- ,
where integer can be at least one member of {1, 2, 3, 4}.
Hence we can have , where real number satisfies .
(For example:
- for , we have ;
- for , we have ;
- for , we have ;
- for , we have .)
-
- =
- =
- =
- = 1 + 0 + 0
- = 1 .
Written on Aug 12 2021