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Search: id:A145800
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| A145800 |
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a(n) = the smallest positive integer that is a (odd) palindrome when represented in binary and that contains within it the binary representation of n. |
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+0
4
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| 1, 5, 3, 9, 5, 27, 7, 17, 9, 21, 27, 51, 27, 93, 15, 33, 17, 73, 51, 165, 21, 45, 93, 99, 51, 107, 27, 231, 93, 189, 31, 65, 33, 273, 99, 73, 165, 153, 231, 325, 165, 85, 107, 717, 45, 93, 189, 195, 99, 403, 51, 843, 107, 219, 119, 455, 231, 471, 119, 633, 189, 381, 63
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For n = power of 2, a(n) = 2*n + 1.
This sequence contains, by definition, those binary palindromes that are odd, ie those palindromes without leading zeros. In other words, only integers occurring in sequence A006995 occur in this sequence.
a(A006995(n)) = A006995(n). [From Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 26 2008]
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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6 in binary is 110. Those integers which contain 110 in their binary representations are 6 (110 in binary), 12 (1100 in binary), 13 (1101 in binary), 14 (1110 in binary), 22 (10110 in binary), 24 (11000 in binary), 25 (11001 in binary), 26 (11010 in binary), 27 (11011 in binary), etc... Now, 27 (11011 in binary) is the smallest of these integers that is a binary palindrome; so a(6) = 27.
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CROSSREFS
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A006995, A145799
Sequence in context: A128426 A165789 A133090 this_sequence A161501 A118273 A073891
Adjacent sequences: A145797 A145798 A145799 this_sequence A145801 A145802 A145803
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KEYWORD
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base,nonn
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AUTHOR
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Leroy Quet Oct 19 2008
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 26 2008
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