A275342 2-adic valuation of iterated triangular numbers, starting with 2.

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, 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, 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

Offset: 1

Author

Jeffrey Shallit, Jul 23 2016

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A007501, A007814, A117872.

Formula

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.

a(n) = A007814(A007501(n)). - Michel Marcus, Jul 23 2016