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Search: id:A081242
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| A081242 |
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Left-to-right binary enumeration. |
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+0
2
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| 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; listen)
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OFFSET
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2,2
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COMMENT
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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.
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FORMULA
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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.
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EXAMPLE
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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, doing the arithmetic from left to right: e -> 1 -> 2 -> 11 -> 21 -> 22 -> 111 -> 211 -> ...
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CROSSREFS
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Cf. A059893, A007931.
Sequence in context: A061907 A052216 A094629 this_sequence A071762 A113721 A127199
Adjacent sequences: A081239 A081240 A081241 this_sequence A081243 A081244 A081245
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KEYWORD
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base,nonn,word
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Mar 12 2003
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