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%I #6 Mar 30 2012 18:57:05
%S 1,2,11,21,12,22,111,211,121,221,112,212,122,222,1111,2111,1211,2211,
%T 1121,2121,1221,2221,1112,2112,1212,2212,1122,2122,1222,2222,11111,
%U 21111,12111,22111,11211,21211,12211,22211,11121,21121,12121,22121
%N Left-to-right binary enumeration.
%C 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.
%F 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.
%e 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 e -> 1 -> 2 -> 11 -> 21 -> 12 -> 22 -> 111 -> 211 -> 121 -> 221
%Y Cf. A059893, A007931.
%K base,nonn,word
%O 2,2
%A _Clark Kimberling_, Mar 12 2003
%E Example edited by _Franklin T. Adams-Watters_, Jan 25 2010
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