A274950 Trajectory of 0 under the morphism 0 -> 0001101, 1 -> 0011001.

0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0

Offset

0

Comments

In some bar codes, the 0's and 1's on the left represent digits according to the following code:

0 = 0001101,

1 = 0011001,

2 = 0010011,

...,

9 = 0001011.

This sequence could then be loosely described as its own bar code.

(This assumes the sequence has no "guard digits" at the start, is infinite, and only uses the "left half" coding.)

Links

David A. Corneth, Table of n, a(n) for n = 0..10002

Index entries for sequences that are fixed points of mappings

Example

Start with 0 -> 0001101, so we have 0001101. The second digit is 0, so we concatenate 0001101 which gives 00011010001101. The third digit is 0, so we concatenate 0001101 again which gives 000110100011010001101. The fourth digit is 1 so we concatenate 0011001 to get 0001101000110100011010011001, etc. - David A. Corneth, Aug 03 2017

Mathematica

Nest[Flatten[# /. {0 -> {0, 0, 0, 1, 1, 0, 1}, 1 -> {0, 0, 1, 1, 0, 0, 1}}] &, 0, 3] (* Michael De Vlieger, Aug 03 2017 *)

Prog

(PARI) first(n) = {my(res = [0, 0, 0, 1, 1, 0, 1], i = 2, m = Map(Mat([0, [0, 0, 0, 1, 1, 0, 1]; 1, [0, 0, 1, 1, 0, 0, 1]]))); while(#res < n, res = concat(res, mapget(m, res[i])); i++); res} \\ David A. Corneth, Aug 03 2017

Crossrefs

Cf. A191818.

Sequence in context: A011658 A135461 A327219 * A093383 A093384 A080584

Adjacent sequences: A274947 A274948 A274949 * A274951 A274952 A274953

Keyword

nonn

Author

N. J. A. Sloane, Aug 04 2016

Status

approved