CARLOS LIÑÁN REYES

An improvement of the Krasikov–Lagarias lower bound for the 3x+1 problem: π_a(x) ≥ Δ·x^0.8892

Let π_a(x) be the number of integers n ≤ x whose 3x+1 trajectory reaches a. Krasikov and Lagarias (Acta Arith. 109, 2003) proved π_a(x) ≥ Δ·x^0.84 for a ≢ 0 (mod 3) via a feasible solution of their nonlinear program L_11^NT(λ); that exponent has remained the published record (cit...