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

1,1

Comments

The terminating empty word is included in the count.

Links

Table of n, a(n) for n=1..23.

Example

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.

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;

Crossrefs

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

Sequence in context: A097511 A200592 A021027 * A359864 A361849 A339409

Adjacent sequences: A289669 A289670 A289671 * A289673 A289674 A289675

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 29 2017

Extensions

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

Status

approved