A289672 - OEIS

%I #25 Jul 31 2017 07:01:09

%S 4,3,4,7,8,7,14,15,14,15,16,15,24,25,28,29,30,35,38,39,38,39,38

%N 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 The terminating empty word is included in the count.

%e For length n=2, there are two words which cycle, 10 and 11:

%e 10 -> 101 -> 1101 -> 11101 -> 011101 -> 10100 -> 001101 -> 10100, which has entered a cycle.

%p # Uses procedures f1 and P from A289670.

%p # Count strings of length n which terminate and which cycle

%p # Print max length to reach empty word (mx)

%p mx:=[];

%p for n from 1 to 11 do

%p lprint("starting length ",n);

%p m:=0;

%p for n1 from 0 to 2^n-1 do

%p t1:=convert(2^n+n1,base,2); t2:=[seq(t1[i],i=1..n)];

%p map(x->convert(x,string),t2); t3:=Join(%,""); t4:=P(%);

%p if t4 <> 999 then if t4>m then m:=t4; fi; fi;

%p od;

%p mx:=[op(mx),m];

%p od:

%p mx;

%Y Cf. A284116, A284119, A284121, A289670, A289671, A289673, A289674, A289675.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Jul 29 2017

%E a(12)-a(23) from _Indranil Ghosh_, Jul 30 2017