|
%I #35 Jan 04 2021 08:44:21
%S 0,1,2,3,2,3,6,7,2,3,6,7,10,11,14,15,2,3,6,7,18,19,22,23,10,11,14,15,
%T 26,27,30,31,2,3,6,7,18,19,22,23,34,35,38,39,50,51,54,55,10,11,14,15,
%U 26,27,30,31,42,43,46,47,58,59,62,63,2,3,6,7,18,19,22,23
%N Milk shuffle of the binary representation of n.
%H Sander G. Huisman, <a href="/A339132/b339132.txt">Table of n, a(n) for n = 0..5000</a> [a(0)=0 inserted by _Georg Fischer_, Jan 04 2021]
%H Roger Antonsen, <a href="https://archive.bridgesmathart.org/2018/bridges2018-451.html">Card Shuffling Visualizations</a>, Bridges Conference Proceedings, 2018.
%e For n = 19 we take the binary representation without leading zeros: 10011.
%e We now shuffle the binary digits around according to A209279, which can be interpreted as a so-called milk shuffle.
%e For five digits the n-th digits gets moved around as follows: 1,2,3,4,5 => 3,2,4,1,5.
%e This reshuffling can be thought of taking the middle number, and then alternatingly taking digits from the left and then the right until all digits are taken.
%e We now apply this reshuffling to our binary digits of 19: 00111.
%e This is now reinterpreted into a decimal number: 7.
%t milk[list_]:=Table[list[[{i,-i}]],{i,Length[list]/2}]//milkPost[#,list]&//Reverse//Flatten
%t milkPost[x_,list_]:=x/;EvenQ[Length[list]]
%t milkPost[x_,list_]:=Join[x,{list[[(Length[list]+1)/2]]}]
%t Table[FromDigits[milk@IntegerDigits[i,2],2],{i,0,500}]
%t (*OR*)
%t Table[FromDigits[ResourceFunction["Shuffle"][IntegerDigits[i,2],"Milk"],2], {i,0,500}]
%Y Cf. A330090 (shuffle bits low to high).
%Y Cf. A209279 (1-based shuffle), A332104 (0-based shuffle).
%K base,easy,look,nonn
%O 0,3
%A _Sander G. Huisman_, Nov 24 2020
|
