# Strongly sufficient sets and the distribution of arithmetic sequences in the 3x+1 graph

@article{Monks2012StronglySS, title={Strongly sufficient sets and the distribution of arithmetic sequences in the 3x+1 graph}, author={Keenan Monks and Kenneth G. Monks and Kenneth M. Monks and Maria Monks}, journal={Discret. Math.}, year={2012}, volume={313}, pages={468-489} }

Abstract The 3 x + 1 conjecture asserts that the T -orbit of every positive integer contains 1 , where T maps x ↦ x / 2 for x even and x ↦ ( 3 x + 1 ) / 2 for x odd. A set S of positive integers is sufficient if the orbit of each positive integer intersects the orbit of some member of S . Monks (2006) [8] showed that every infinite arithmetic sequence is sufficient. In this paper we further investigate the concept of sufficiency. We construct sufficient sets of arbitrarily low asymptotic… CONTINUE READING

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## On the 3x+1 conjecture

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CITES BACKGROUND

## The Collatz conjecture and De Bruijn graphs

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CITES RESULTS & METHODS

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