#!/usr/bin/env python3
"""Auto-generated by AGI Loop cycle #1100
Task: Write a Python function that generates Fibonacci numbers and shows phi convergence for 20 terms
Generated: 2026-02-12T20:17:43.455080
"""

import sys

def fibonacci_phi_convergence(n_terms=20):
    fib_sequence = [0, 1]
    for i in range(2, n_terms):
        next_term = fib_sequence[-1] + fib_sequence[-2]
        fib_sequence.append(next_term)
    
    phi_convergence = []
    for i in range(2, n_terms):
        phi = fib_sequence[i] / fib_sequence[i-1]
        phi_convergence.append(phi)
    
    print("Fibonacci Sequence (first 20 terms):")
    print(fib_sequence)
    print("\nConvergence to Phi (golden ratio) for each pair:")
    for i, phi in enumerate(phi_convergence):
        print(f"Term pair {i+2} and {i+1}: Phi ≈ {phi:.6f}")

if __name__ == '__main__':
    fibonacci_phi_convergence()