# The sufficiency of arithmetic progressions for the 3x + 1 Conjecture

@inproceedings{Monks2006TheSO, title={The sufficiency of arithmetic progressions for the 3x + 1 Conjecture}, author={Kenneth M. Monks}, year={2006} }

Define T: Z + → Z + by T(x) = (3x+1)/2 if x is odd and T (x) = x/2 if x is even. The 3x +1 Conjecture states that the T-orbit of every positive integer contains 1. A set of positive integers is said to be sufficient if the T-orbit of every positive integer intersects the T-orbit of an element of that set. Thus to prove the 3x+1 Conjecture it suffices to prove it on some sufficient set. Andaloro proved that the sets 1 + 2 n N are sufficient for n < 4 and asked if 1 + 2 n N is also sufficient for… Expand

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E-mail address: monksk2@scranton

- E-mail address: monksk2@scranton

E-mail address: monksk2@scranton.edu License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use

- E-mail address: monksk2@scranton.edu License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use

MONKS

- MONKS

Real 3 x + 1

- Proc . Amer . Math . Soc .