

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.


6



4, 3, 4, 7, 8, 7, 14, 15, 14, 15, 16, 15, 24, 25, 28, 29, 30, 35, 38, 39, 38, 39, 38
(list;
graph;
refs;
listen;
history;
text;
internal format)



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^n1 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 * A075246 A257840 A132984
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



