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A055945 a(n) = n - (reversal of base-2 digits of n) (and then the result is written in base 10).

%I A055945 #34 Apr 28 2025 12:19:22
%S A055945 0,0,1,0,3,0,3,0,7,0,5,-2,9,2,7,0,15,0,9,-6,15,0,9,-6,21,6,15,0,21,6,
%T A055945 15,0,31,0,17,-14,27,-4,13,-18,35,4,21,-10,31,0,17,-14,45,14,31,0,41,
%U A055945 10,27,-4,49,18,35,4,45,14,31,0,63,0,33,-30,51,-12,21,-42,63,0,33,-30,51,-12,21,-42,75,12,45,-18,63,0,33,-30,75,12,45
%N A055945 a(n) = n - (reversal of base-2 digits of n) (and then the result is written in base 10).
%C A055945 a(n) is even if n is odd and a(n) is odd if n is even; this is caused by the kind of swapping the most significant and least significant binary digit when reversing n and the fact that the most significant digit of n is always 1. - _R. J. Mathar_, Nov 05 2015
%H A055945 Alois P. Heinz, <a href="/A055945/b055945.txt">Table of n, a(n) for n = 0..16384</a>
%H A055945 Rémy Sigrist, <a href="/A055945/a055945.png">Colored scatterplot of the first 2^16 terms</a> (where the color is function of n mod 8)
%F A055945 For 2^m <= n <= 2^(m+1), we have n - 2^(m+1) <= a(n) <= n. - _N. J. A. Sloane_, May 29 2016
%F A055945 a(n) = n - A030101(n).
%p A055945 a:= proc(n) local m, r; m:=n; r:=0;
%p A055945       while m>0 do r:= r*2 +irem(m, 2, 'm') od;
%p A055945       n-r
%p A055945     end:
%p A055945 seq(a(n), n=0..100);  # _Alois P. Heinz_, Jul 02 2015
%t A055945 Array[# - IntegerReverse[#, 2] &, 90, 0] (* _Michael De Vlieger_, Sep 06 2019 *)
%Y A055945 Cf. A030101, A030109, A265326.
%K A055945 base,sign,look
%O A055945 0,5
%A A055945 _Henry Bottomley_, Jul 18 2000