%I #6 Jul 23 2016 20:50:03
%S 1,0,1,0,0,2,1,0,0,0,0,2,1,0,1,0,0,0,3,2,1,0,0,2,1,0,1,0,0,0,2,1,0,0,
%T 0,1,0,0,1,0,2,1,0,0,2,1,0,2,1,0,0,2,1,0,0,0,3,2,1,0,1,0,1,0,0,0,0,1,
%U 0,0,1,0,0,0,0,2,1,0,0,0,1,0,0,2,1,0,1,0,3,2,1,0,0,0,1,0,0,0,2,1,0,2,1,0,0,0,0,2,1,0,0,4,3,2,1,0,0,4,3,2,1,0,2,1,0,1,0,0,0,1
%N 2-adic valuation of iterated triangular numbers, starting with 2.
%F Writing t(1) = 2, t(n+1) = t(n)(t(n)+1)/2, the sequence is nu_2 (t(n)), where nu_2 (x) is the exponent of the highest power of 2 dividing x.
%F a(n) = A007814(A007501(n)). - _Michel Marcus_, Jul 23 2016
%e t(1) = 2, t(2) = 3, t(3) = 6, t(4) = 21, so a(1) = 1, a(2) = 0, a(3) = 1, a(4) = 0.
%Y Cf. A007501, A007814, A117872.
%K nonn
%O 1,6
%A _Jeffrey Shallit_, Jul 23 2016