%N Let f(n, x) = x+3x^2+6x^3+...+(n(n+1)/2)x^n; then a(n) = least x such that f(n, x) is a triangular number, or 0 if no such x exists.
%C If k is a member of A027568 (both triangular and tetrahedral) then k = A000292(n-1) for some n and a(n) = 1.
%C Zero values are conjectures. I have searched for a(4) up to x = 10^7, a(5) up to x = 10^6 and the rest up to x = 10^4. (Wasserman)
%Y Cf. A087702.
%A _Amarnath Murthy_, Sep 26 2003
%E Edited and extended by _David Wasserman_, Jun 16 2005