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A330717
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a(n) is the greatest binary palindrome of the form floor(n/2^k) with k >= 0.
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1
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0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 3, 7, 15, 1, 17, 9, 9, 5, 21, 5, 5, 3, 3, 3, 27, 7, 7, 15, 31, 1, 33, 17, 17, 9, 9, 9, 9, 5, 5, 21, 21, 5, 45, 5, 5, 3, 3, 3, 51, 3, 3, 27, 27, 7, 7, 7, 7, 15, 15, 31, 63, 1, 65, 33, 33, 17, 17, 17, 17, 9, 73, 9, 9, 9, 9
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OFFSET
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0,4
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COMMENTS
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In other words, a(n) is the greatest binary palindromic prefix of n.
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LINKS
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FORMULA
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a(n) = 1 iff n is a power of 2.
a(n) <= n with equality iff n is a binary palindrome (A006995).
a(a(n)) = a(n).
a(2*n) = a(n).
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EXAMPLE
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The first terms, alongside the binary representations of n and of a(n), are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0 0 0
1 1 1 1
2 1 10 1
3 3 11 11
4 1 100 1
5 5 101 101
6 3 110 11
7 7 111 111
8 1 1000 1
9 9 1001 1001
10 5 1010 101
11 5 1011 101
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PROG
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(PARI) a(n, b=2) = { my (d=digits(n, b)); forstep (w=#d, 1, -1, my (h=d[1..w]); if (h==Vecrev(h), return (fromdigits(h, b)))); return (0) }
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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