The sequence {A_n, n ≥ 0} is defined by:

A₀ = 0, and:

A_n+1 = [³√(A_n + n)]³

Determine an explicit formula representing A_n in terms of n.

Hence, or otherwise, determine all n such that A_n = n

Note: [x] represents the greatest integer ≤ x

(In reply to Question? by broll)

Note there is a floor function there. The square brackets are not there to provide visual distinction from the internal parentheses, but rather, as the note explains, indicate the floor of their contents, which, for the positive numbers involved here, amounts to truncating to an integer.

Posted by Charlie on 2011-02-03 14:01:57