@article{BenAmram1996ANO,
title={A note on busy beavers and other creatures},
author={Amir M. Ben-Amram and Bryant A. Julstrom and Uri Zwick},
journal={Mathematical systems theory},
year={1996},
volume={29},
pages={375-386}
}

Consider Turing machines that read and write the symbols 1 and 0 on a one-dimensional tape that is infinite in both directions, and halt when started on a tape containing all O's. Rado'sbusy beaver function ones(n) is the maximum number of 1's such a machine, withn states, may leave on its tape when it halts. The function ones(n) is noncomputable; in fact, it grows faster than any computable function. Other functions with a similar nature can also be defined. The function time(n) is the maximum… CONTINUE READING