JumpCycleSteps

Jump.py

import math

def jump_cycle_steps(k, x0, n):
    # Theoretical number of steps until repeat
    steps_expected = n // math.gcd(k, n)
    print(f"Modulus (n): {n}")
    print(f"Jump size (k): {k}")
    print(f"Start at x0: {x0}")
    print(f"GCD(k, n): {math.gcd(k, n)}")
    print(f"Expected cycle length: {steps_expected}")

    # Simulate the jumps
    seen = set()
    x = x0
    steps = 0

    while x not in seen:
        seen.add(x)
        x = (x + k) % n
        steps += 1

    print(f"Simulated steps to return: {steps}")
    print(f"Returned to start: {x == x0}")
    return steps

# Example usage
k = 45
x0 = 0
n = 45 ** 3

jump_cycle_steps(k, x0, n)