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Search: id:A145799
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| A145799 |
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a(n) = the largest integer that is a (odd) palindrome when represented in binary and that occurs in the binary representation of n. |
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+0
2
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| 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 5, 7, 15, 1, 17, 9, 9, 5, 21, 5, 7, 3, 9, 5, 27, 7, 7, 15, 31, 1, 33, 17, 17, 9, 9, 9, 9, 5, 9, 21, 21, 5, 45, 7, 15, 3, 17, 9, 51, 5, 21, 27, 27, 7, 9, 7, 27, 15, 15, 31, 63, 1, 65, 33, 33, 17, 17, 17, 17, 9, 73, 9, 9, 9, 9, 9, 15, 5, 17, 9, 9, 21, 85, 21, 21
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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For n = power of 2, n >= 4, the longest-lengthed binary palindrome is a string of 0's and is the numerical equivalent of 0 (with leading 0's). But for n = power of 2, 1 is always the numerically largest binary palindrome included in the binary representation of n.
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(2^k*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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20 in binary is 10100. The largest binary palindrome included in this binary representation is 101, which is 5 in decimal. So a(20) = 5.
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CROSSREFS
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A006995, A145800
Sequence in context: A161825 A099551 A036233 this_sequence A098985 A072963 A161955
Adjacent sequences: A145796 A145797 A145798 this_sequence A145800 A145801 A145802
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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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