Collatz conjecture dataset

This data set includesCollatz steps for 2-10000· r23 (base-2/3 exact resonance): The total number of steps in the trajectory where the digit sum in base 2 exactly equals the digit sum in base 3.· nr23 (base-2/3 near-resonance): The total number of steps where the absolute difference between the base-2 digit sum and the base-3 digit sum is exactly 1.· r35/r37/r57 (cross-base resonance counters): Cumulative counters tracking how often the digit sums of two different prime bases (e.g., base 3 and base 5) align during the trajectory.For example, the Collatz trajectory for N=7 dynamically transforms as follows, generating specific digit sums sb in each prime base at every transition point:Initial State ((N=7):· Binary representation: 111 (base 2) implies s2=3· Ternary representation: (21 (base 3) implies s3=3· Base-5 representation: (12 (base 5)implies s5=3· Base-7 representation: (10 (base 7) implies s7=1Since s2=s3, (3=3), r23 increments by 1. Since s3=s5, (3=3), r35 increments by 1.Next State ((N = 22 =3x7+1):· s2=3 (10110 (base 2))· s3= 4 (211 (base 3))· s5=6 (42 (base 5))· s7=4 (31 (base 7))And so on.