

A289673


Take nth string over {1,2} in lexicographic order and apply the Post tag system described in A284116 (but adapted to the alphabet {1,2}) just once.


10



1, 12, 1, 1, 212, 212, 11, 11, 11, 11, 2212, 2212, 2212, 2212, 111, 211, 111, 211, 111, 211, 111, 211, 12212, 22212, 12212, 22212, 12212, 22212, 12212, 22212, 1111, 1211, 2111, 2211, 1111, 1211, 2111, 2211, 1111, 1211, 2111, 2211, 1111, 1211, 2111, 2211, 112212
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OFFSET

1,2


COMMENTS

Post's tag system maps a word w over {1,2} to w', where if w begins with 1, w' is obtained by appending 11 to w and deleting the first three letters, or if w begins with 2, w' is obtained by appending 2212 to w and deleting the first three letters.
The empty word is denoted by 1.
We work over {1,2} rather than the official alphabet {0,1} because of the prohibition in the OEIS of terms (other than 0 itself) which begin with 0.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000


EXAMPLE

The initial words are:
1,2,11,12,21,22,111,112,121,122,211,212,221,222,1111,...
Applying the tag system over {1,2} these become:
1, 12, 1, 1, 212, 212, 11, 11, 11, 11, 2212, 2212, 2212, 2212, 111, ...
If we were working over {0,1} the initial strings would be:
0,1,00,01,10,11,000,001,010,011,100,101,110,111,0000,...
and applying the tag system over {0,1} described in A284116 these would become:
1, 01, 0, 0, 101, 101, 00, 00, 00, 00, 1101, 1101, 1101, 1101, 000, ...


MAPLE

See A291072.


PROG

(Python)
from itertools import product
A289673_list = [1 if s == ('1', ) else int((''.join(s)+('2212' if s[0] == '2' else '11'))[3:]) for l in range(1, 10) for s in product('12', repeat=l)] # Chai Wah Wu, Aug 06 2017


CROSSREFS

Cf. A284116, A284119, A284121, A289670, A289671, A289672, A289674, A289675.
See also A291072, A291073, A291074.
Sequence in context: A176627 A015129 A172376 * A010211 A066786 A109015
Adjacent sequences: A289670 A289671 A289672 * A289674 A289675 A289676


KEYWORD

sign


AUTHOR

N. J. A. Sloane, Jul 29 2017


EXTENSIONS

More terms from Chai Wah Wu, Aug 06 2017


STATUS

approved



