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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.
7
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.
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;
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Jul 29 2017
EXTENSIONS
a(12)-a(23) from Indranil Ghosh, Jul 30 2017
STATUS
approved