A081242 Left-to-right binary enumeration.

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

Offset: 2

Author

Clark Kimberling, Mar 12 2003

Keywords

• base
• nonn
• word

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.

Examples

			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

Cf. A059893, A007931.

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.

Extensions

Example edited by Franklin T. Adams-Watters, Jan 25 2010