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Theoretical analysis reveals super-polynomial growth in prime-support totient recurrences, indicating novel nonautonomous arithmetic dynamics across integer intervals.
This paper introduces and analyzes Prime-Support Totient Recurrences (PSTR), a novel class of nonautonomous arithmetic dynamics generated by coupling Euler's totient function to the prime support across short integer intervals. We establish the mathematical framework for the primary sequence aₙ, prove its initial structural properties, and analyze its super-polynomial growth regime. In addition to exact numerical computations and empirical prime factorizations for the first several terms, we formulate the generalized PSTR family, explore its dynamic prime-factor dependence, and outline key open problems regarding term density and asymptotic bounds.
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Serdar Ali Toker (2026) studied this question.
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