

A081242


Lefttoright binary enumeration.


3



1, 2, 11, 21, 12, 22, 111, 211, 121, 221, 112, 212, 122, 222, 1111, 2111, 1211, 2211, 1121, 2121, 1221, 2221, 1112, 2112, 1212, 2212, 1122, 2122, 1222, 2222, 11111, 21111, 12111, 22111, 11211, 21211, 12211, 22211, 11121, 21121, 12121, 22121
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OFFSET

2,2


COMMENTS

In A007931, the arithmetic is done from right to left, yielding reversals of the terms of A081242. In A007931, new wordlengths occur at 1,3,7,15,...; in A081242, they occur at 2,4,8,16,.... In A007931, indexing starts at 1 and the sequence is numerical; in A081242, indexing starts at 2, leaving room for the empty word at position 1 and the sequence consists of all binary words.


LINKS



FORMULA

Write n in base 2, remove initial 1, add 1 to remaining digits and reverse their order. Or, start with empty word e, follow by 1 and then successively add 1, always working from left to right.


EXAMPLE

Eleven in base 2 is 1011; remove initial 1 to have 011; add 1 to all digits to have 122; reverse those to have a(11)=221. Or, start with the empty word and add 1's successively, using digits 1 and 2, and doing the arithmetic from left to right:
e > 1 > 2 > 11 > 21 > 12 > 22 > 111 > 211 > 121 > 221


CROSSREFS



KEYWORD

base,nonn,word


AUTHOR



EXTENSIONS



STATUS

approved



