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Search: id:A165199
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| A165199 |
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Let b(n,m) be the mth digit, reading left to right, of binary n. (b(n, 1) is the most significant binary digit, which is 1.) Then a(n) is such that b(a(n),1)=1; and if b(n,m)=b(n,m-1) then b(a(n),m) does not = b(a(n),m-1); and if b(n,m) does not = b(n,m-1) then b(a(n), m) = b(a(n),m-1), for all m where 2 <= m <= number binary digits in n. |
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| 1, 3, 2, 6, 7, 4, 5, 13, 12, 15, 14, 9, 8, 11, 10, 26, 27, 24, 25, 30, 31, 28, 29, 18, 19, 16, 17, 22, 23, 20, 21, 53, 52, 55, 54, 49, 48, 51, 50, 61, 60, 63, 62, 57, 56, 59, 58, 37, 36, 39, 38, 33, 32, 35, 34, 45, 44, 47, 46, 41, 40, 43, 42, 106, 107, 104, 105, 110, 111, 108
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is a self-inverse permutation of the positive integers.
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EXAMPLE
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12 in binary is 1100. Generating a(12): the leftmost binary digit is 1. In 1100, the 2nd digit from the left equals the first, so the second digit from the left of binary a(12) does not equal the first; so we have 10 as the two leftmost digits in binary a(12). The third digit from the left of binary 12 does not equal the second, so the third digit from the left of binary a(12) equals the second; therefore the leftmost 3 digits of a(12) in binary are 100. And finally, the rightmost digit of binary 12 equals the 3rd from the left, so the rightmost digit of binary a(12) does not equal the 3rd from the left of binary a(12). Therefore a(12) in binary is 1001. And a(12) is the decimal equivalent of this, which is 9.
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CROSSREFS
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Sequence in context: A154446 A154442 A154445 this_sequence A120231 A083362 A153142
Adjacent sequences: A165196 A165197 A165198 this_sequence A165200 A165201 A165202
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KEYWORD
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base,nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Sep 07 2009
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 10 2009
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