[seqfan] Re: Patterns of congruence classes modulo 2^n in reduced Collatz sequences

[L. Edson Jeffery]

Bob,

Let N_1 denote the set of odd natural numbers. Assuming the Collatz
conjecture, then your triangle is the result of iterating the function F,
defined in Chamberland [1] (and probably elsewhere), and terminating each
sequence at the first occurrence of 1, where

   F(x) = (3*x+1)/2^|3*x+1|_2,

for each x in N_1, and |y|_p is Donald Knuth's symbol for p-adic valuation
of y, for p a prime.

[1] M. Chamberland, Una actualizacio del problema 3x + 1, Butl. Soc.
Catalana Mat. (18), 19--45, 2003.


Ed Jeffery