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%I #24 Apr 26 2020 03:41:35
%S 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,
%T 22,27,28,23,30,31,32,33,34,49,36,41,50,57,40,37,42,53,52,45,58,61,48,
%U 35,38,51,44,43,54,59,56,39,46,55,60,47,62,63,64,65,66,97,68,81,98,113
%N Bit-reverse of n, including as many leading as trailing zeros.
%C 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
%C 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).
%H N. J. A. Sloane, <a href="/A057889/b057889.txt">Table of n, a(n) for n = 0..16384</a>, May 30 2016 [First 8192 terms from _Ivan Neretin_, Jul 09 2015]
%F a(n) = A030101(A000265(n)) * A006519(n), with a(0)=0.
%e a(6)=6 because 0110 is a palindrome, but a(11)=13 because 1011 reverses into 1101.
%t Table[FromDigits[Reverse[IntegerDigits[n, 2]], 2]*2^IntegerExponent[n, 2], {n, 71}] (* _Ivan Neretin_, Jul 09 2015 *)
%o (Python)
%o def a(n):
%o x = bin(n)[2:]
%o y = x[::-1]
%o return int(str(int(y))+(len(x) - len(str(int(y))))*'0', 2)
%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 11 2017
%Y Cf. A030101, A000265, A006519, A006995, A057890, A057891.
%K easy,nonn,base,look
%O 0,3
%A _Marc LeBrun_, Sep 25 2000
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