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A081242 Left-to-right binary enumeration. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=2..43.

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

Cf. A059893, A007931.

Sequence in context: A061907 A052216 A094629 * A071762 A288945 A245500

Adjacent sequences:  A081239 A081240 A081241 * A081243 A081244 A081245

KEYWORD

base,nonn,word

AUTHOR

Clark Kimberling, Mar 12 2003

EXTENSIONS

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

STATUS

approved

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Last modified February 18 19:50 EST 2019. Contains 320262 sequences. (Running on oeis4.)