Averaged meta-Fibonacci recursions at critical alpha=1 exhibit a triangular block structure where k appears k times, yielding Q(n) ~ sqrt(2n), while supercritical alpha>1 forces any linear growth rate to equal 1 - 1/alpha.
Hofstadter.G¨ odel, Escher, Bach: An Eternal Golden Braid
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The parity-perturbed Hofstadter recursion Q(n) = Q(n-Q(n-1)) + Q(n-Q(n-2)) + (-1)^n with Q(1)=Q(2)=1 is shown to be well-defined for all n ≥ 1 via certified finite-state induction.
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Critical Slow Growth in Averaged Meta-Fibonacci Recursions
Averaged meta-Fibonacci recursions at critical alpha=1 exhibit a triangular block structure where k appears k times, yielding Q(n) ~ sqrt(2n), while supercritical alpha>1 forces any linear growth rate to equal 1 - 1/alpha.
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Certified Finite-State Induction for a Perturbed Hofstadter Recursion
The parity-perturbed Hofstadter recursion Q(n) = Q(n-Q(n-1)) + Q(n-Q(n-2)) + (-1)^n with Q(1)=Q(2)=1 is shown to be well-defined for all n ≥ 1 via certified finite-state induction.