cp's OEIS Frontend

A289672 Consider the Post tag system defined in A284116; a(n) = maximum, taken over all binary words w of length n which terminate in a cycle, of the number of words in the orbit of w.

%I A289672 #25 Jul 31 2017 07:01:09
%S A289672 4,3,4,7,8,7,14,15,14,15,16,15,24,25,28,29,30,35,38,39,38,39,38
%N A289672 Consider the Post tag system defined in A284116; a(n) = maximum, taken over all binary words w of length n which terminate in a cycle, of the number of words in the orbit of w.
%C A289672 The terminating empty word is included in the count.
%e A289672 For length n=2, there are two words which cycle, 10 and 11:
%e A289672 10 -> 101 -> 1101 -> 11101 -> 011101 -> 10100 -> 001101 -> 10100, which has entered a cycle.
%p A289672 # Uses procedures f1 and P from A289670.
%p A289672 # Count strings of length n which terminate and which cycle
%p A289672 # Print max length to reach empty word (mx)
%p A289672 mx:=[];
%p A289672 for n from 1 to 11 do
%p A289672 lprint("starting length ",n);
%p A289672 m:=0;
%p A289672 for n1 from 0 to 2^n-1 do
%p A289672 t1:=convert(2^n+n1,base,2); t2:=[seq(t1[i],i=1..n)];
%p A289672 map(x->convert(x,string),t2); t3:=Join(%,""); t4:=P(%);
%p A289672 if t4 <> 999 then if t4>m then m:=t4; fi; fi;
%p A289672 od;
%p A289672 mx:=[op(mx),m];
%p A289672 od:
%p A289672 mx;
%Y A289672 Cf. A284116, A284119, A284121, A289670, A289671, A289673, A289674, A289675.
%K A289672 nonn,more
%O A289672 1,1
%A A289672 _N. J. A. Sloane_, Jul 29 2017
%E A289672 a(12)-a(23) from _Indranil Ghosh_, Jul 30 2017