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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

%I #14 Sep 13 2021 09:17:34

%S 6,21,16,31,412,57,2156,859,382,2811,372,2609,704,37913,618,155,1008,

%T 2407,1210,629,5286,1779,1468,4346275,4130,3247,7024,3891,14638,7025,

%U 4570,4329,147694,1863,11126,81147,20210,3853,116020,7641,6494

%N 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.

%C a(n) = A284119(n) + A284121(n) (or -1 if the trajectory is unbounded).

%C a(n) is a lower bound on A284116(3n) (assuming that there is no starting string with an unbounded trajectory).

%C 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

%H Lars Blomberg, <a href="/A302202/b302202.txt">Table of n, a(n) for n = 1..6075</a>

%Y Cf. A284119, A284121; A284116.

%K nonn

%O 1,1

%A _Lars Blomberg_ and _N. J. A. Sloane_, Apr 19 2018

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