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- W2169284412 abstract "The generalized Collatz problem (also called the px+q problem with p an odd prime and q odd) is defined by a sequence of natural numbers, generated conditionally by xn+1 = 1 2xn if xn is even and by xn+1 = 12 (pxn+q) if xn is odd [4]. Empirically px+q problems show for p ≥ 5 mostly divergent trajectories and exceptionally cyclic behavior. We prove for each p : (i) There exist infinitely many px + q problems with a primitive 1-cycle, (ii) There exist infinitely many px + q problems with an arbitrary number of primitive cycles, (iii) Under a mild number theoretical condition, we can construct infinitely many px+ q problems (p and q prime) with arbitrarily many primitive cycles. Mathematics Subject Classifications 11B83, 11J86" @default.
- W2169284412 created "2016-06-24" @default.
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- W2169284412 date "2008-01-01" @default.
- W2169284412 modified "2023-10-18" @default.
- W2169284412 title "Exotic Collatz cycles" @default.
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- W2169284412 doi "https://doi.org/10.4064/aa134-3-1" @default.
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