OFFSET
0,1
COMMENTS
There are 3 states. Start in state A.
If in A and 0 arrives go to A
If in A and 1 arrives go to B
If in B and 0 arrives go to C
If in B and 1 arrives go to A
If in C and 0 arrives go to A
If in C and 1 arrives go to C
If end in A, B, C then output 0, 0, 1 respectively.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
J.-P. Allouche and M. Mendes France, Automata and Automatic Sequences, in: Axel F. and Gratias D. (eds), Beyond Quasicrystals. Centre de Physique des Houches, vol 3. Springer, Berlin, Heidelberg, pp. 293-367, 1995; DOI https://doi.org/10.1007/978-3-662-03130-8_11.
J.-P. Allouche and M. Mendes France, Automata and Automatic Sequences, in: Axel F. and Gratias D. (eds), Beyond Quasicrystals. Centre de Physique des Houches, vol 3. Springer, Berlin, Heidelberg, pp. 293-367, 1995; DOI https://doi.org/10.1007/978-3-662-03130-8_11. [Local copy]
EXAMPLE
a(10) = 1: 10 = 1010, read from right: A->A->B->C, so output a 1.
MAPLE
T:= <<1, 3, 1>|<2, 1, 3>>:
a:= proc(n)
local L, state, i;
L:= convert(n, base, 2);
state:= 1;
for i from 1 to nops(L) do
state:= T[state, L[i]+1];
od:
[0, 0, 1][state];
end proc:
seq(a(n), n=0..100); # Robert Israel, Aug 18 2014
PROG
(PARI) {m=104; for(n=0, m, tape=binary(n); d=length(tape); state="A"; for(j=0, d-1, in=tape[d-j];
state=if(state=="A", if(in==0, "A", "B"), if(state=="B", if(in==0, "C", "A"), if(in==0, "A", "C"))));
print1(if(state=="A"||state=="B", 0, 1), ", "))} \\ Klaus Brockhaus, Jun 23 2004
(Haskell)
a094912 n = a 2 n where
a s 0 = 0 ^ s
a s x = a (t s b) x' where (x', b) = divMod x 2
t 2 0 = 2; t 2 1 = 1; t 1 0 = 0; t 1 1 = 2; t 0 0 = 2; t 0 1 = 0
-- state encoding: A = 2, B = 1, C = 0.
-- Reinhard Zumkeller, Nov 11 2013
(Python)
def delta(q, a):
if q == "A": return {"0": "A", "1": "B"}[a]
if q == "B": return {"0": "C", "1": "A"}[a]
return {"0": "A", "1": "C"}[a]
def a(n):
q = "A"
for a in bin(n)[2:][::-1]: q = delta(q, a)
return int(q == "C")
print([a(n) for n in range(105)]) # Michael S. Branicky, Jul 31 2022
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
N. J. A. Sloane, Jun 21 2004
EXTENSIONS
A very interesting paper. I only looked though it as far as page 12. Perhaps some reader would read to the end and add appropriate references to it from other entries in the OEIS, as well as adding any new sequences that are found. A similar remark could be made about many papers on Jean-Paul Allouche's web site. - N. J. A. Sloane.
More terms from Klaus Brockhaus, Jun 23 2004
STATUS
approved