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A302202
a(n) = number of distinct words arising in Post's tag system {00, 1101} applied to the word (100)^n , or a(n) = -1 if this word has an unbounded trajectory.
1
6, 21, 16, 31, 412, 57, 2156, 859, 382, 2811, 372, 2609, 704, 37913, 618, 155, 1008, 2407, 1210, 629, 5286, 1779, 1468, 4346275, 4130, 3247, 7024, 3891, 14638, 7025, 4570, 4329, 147694, 1863, 11126, 81147, 20210, 3853, 116020, 7641, 6494
OFFSET
1,1
COMMENTS
a(n) = A284119(n) + A284121(n) (or -1 if the trajectory is unbounded).
a(n) is a lower bound on A284116(3n) (assuming that there is no starting string with an unbounded trajectory).
On October 30 2020, a student in my CS 360 class, Zhiping Cai, found that for n = 70051, 96938660265781 (96.9 trillion) steps are needed. See https://github.com/zcai1/posts-problem . I am not sure this has been independently verified. - Jeffrey Shallit, Sep 13 2021
LINKS
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved