A225180 Infinite sequence M defined by the rules M = 1:X, X = 2:zip_2(X,Y), Y = 2:zip_3(M,Y,Y).

1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2

Offset

0,2

Comments

If S, T, U are infinite sequences, zip_2(S,T) means the perfect shuffle S_0, T_0, S_1, T_1, S_2, ... and similarly zip_3(S,T,U) means S_0, T_0, U_0, S_1, ...

The colon means "concatenate".

Endrullis et al. define the sequence over the alphabet {a,b}, getting abbbbabbbbabbababbbbabbbbbabbbabbbbababaabbababbbbbba...

(see also A225181).

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..8191

Jörg Endrullis, Clemens Grabmayer, Dimitri Hendriks, Mix-Automatic Sequences, slides of talk presented at workshop on challenges in combinatorics on words, Fields Institute, Toronto, April 21-26, 2013.

Jörg Endrullis, Clemens Grabmayer, Dimitri Hendriks, Mix-Automatic Sequences, In: Proceedings Conference on Language and Automata Theory and Applications (LATA 2013), Springer, 2013, pages 262-274.

Example

The initial steps in the calculation are:
M := [a]
X := [b]
Y := [b]
X =  [b, b, b]
Y =  [b, a, b, b]
M =  [a, b, b, b]
X =  [b, b, b, b, a, b, b]
Y =  [b, a, b, b, b, a, a, b, b, b, b, b, b]
M =  [a, b, b, b, b, a, b, b]
X =  [b, b, b, b, a, b, b, b, b, a, b, b, a, b, a]
Y =  [b, a, b, b, b, a, a, b, b, b, b, b, b, b, b, b, a, a, a, b, a, a, b, b, b]
M =  [a, b, b, b, b, a, b, b, b, b, a, b, b, a, b, a]
...

Maple

M1:=7;
M:=[a]; X:=[b]; Y:=[b];
for n from 1 to M1 do
l1:=min(nops(X), nops(Y));
t1:=[b];
for i1 from 1 to l1 do
t1:=[op(t1), X[i1], Y[i1]]; od:
X:=t1;
#lprint("X = ", X);
l2:=min(nops(M), nops(Y));
t2:=[b];
for i2 from 1 to l2 do
t2:=[op(t2), M[i2], Y[i2], Y[i2]]; od:
Y:=t2;
#lprint("Y = ", Y);
M:=[a, op(X)];
#lprint("M = ", M);
od:
M;

Crossrefs

Cf. A225181.

Sequence in context: A090044 A036238 A318723 * A276134 A297031 A229895

Adjacent sequences: A225177 A225178 A225179 * A225181 A225182 A225183

Keyword

nonn

Author

N. J. A. Sloane, May 03 2013

Status

approved