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.

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

Offset: 1

Author

N. J. A. Sloane, Jul 29 2017

Keywords

• nonn
• more

Comments

The terminating empty word is included in the count.

Examples

			For length n=2, there are two words which cycle, 10 and 11:
10 -> 101 -> 1101 -> 11101 -> 011101 -> 10100 -> 001101 -> 10100, which has entered a cycle.
		

Crossrefs

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

Programs

Maple

# Uses procedures f1 and P from A289670.
# Count strings of length n which terminate and which cycle
# Print max length to reach empty word (mx)
mx:=[];
for n from 1 to 11 do
lprint("starting length ",n);
m:=0;
for n1 from 0 to 2^n-1 do
t1:=convert(2^n+n1,base,2); t2:=[seq(t1[i],i=1..n)];
map(x->convert(x,string),t2); t3:=Join(%,""); t4:=P(%);
if t4 <> 999 then if t4>m then m:=t4; fi; fi;
od;
mx:=[op(mx),m];
od:
mx;

Extensions

a(12)-a(23) from Indranil Ghosh, Jul 30 2017