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.

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

Lars Blomberg, Table of n, a(n) for n = 1..6075

Crossrefs

Cf. A284119, A284121; A284116.

Sequence in context: A321776 A064929 A298266 * A200831 A184291 A102993

Adjacent sequences: A302199 A302200 A302201 * A302203 A302204 A302205

Keyword

nonn

Author

Lars Blomberg and N. J. A. Sloane, Apr 19 2018

Status

approved