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A057889
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Bit-reverse of n, including as many leading as trailing zeros.
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66
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 12, 11, 14, 15, 16, 17, 18, 25, 20, 21, 26, 29, 24, 19, 22, 27, 28, 23, 30, 31, 32, 33, 34, 49, 36, 41, 50, 57, 40, 37, 42, 53, 52, 45, 58, 61, 48, 35, 38, 51, 44, 43, 54, 59, 56, 39, 46, 55, 60, 47, 62, 63, 64, 65, 66, 97, 68, 81, 98, 113
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listen;
history;
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internal format)
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OFFSET
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0,3
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COMMENTS
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In other words, keep the trailing zeros in the binary expansion of n fixed, but reverse all the digits up to that point. - N. J. A. Sloane, May 30 2016
A permutation of integers consisting only of fixed points and pairs. a(n)=n when n is a binary palindrome (including as many leading as trailing zeros), otherwise a(n)=A003010(n) (i.e. n has no axis of symmetry). A057890 gives the palindromes (fixed points, akin to A006995) while A057891 gives the "antidromes" (pairs).
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LINKS
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FORMULA
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EXAMPLE
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a(6)=6 because 0110 is a palindrome, but a(11)=13 because 1011 reverses into 1101.
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MATHEMATICA
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Table[FromDigits[Reverse[IntegerDigits[n, 2]], 2]*2^IntegerExponent[n, 2], {n, 71}] (* Ivan Neretin, Jul 09 2015 *)
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PROG
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(Python)
def a(n):
x = bin(n)[2:]
y = x[::-1]
return int(str(int(y))+(len(x) - len(str(int(y))))*'0', 2)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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