OFFSET
0,3
LINKS
Sander G. Huisman, Table of n, a(n) for n = 0..5000 [a(0)=0 inserted by Georg Fischer, Jan 04 2021]
Roger Antonsen, Card Shuffling Visualizations, Bridges Conference Proceedings, 2018.
EXAMPLE
For n = 19 we take the binary representation without leading zeros: 10011.
We now shuffle the binary digits around according to A209279, which can be interpreted as a so-called milk shuffle.
For five digits the n-th digits gets moved around as follows: 1,2,3,4,5 => 3,2,4,1,5.
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.
We now apply this reshuffling to our binary digits of 19: 00111.
This is now reinterpreted into a decimal number: 7.
MATHEMATICA
milk[list_]:=Table[list[[{i, -i}]], {i, Length[list]/2}]//milkPost[#, list]&//Reverse//Flatten
milkPost[x_, list_]:=x/; EvenQ[Length[list]]
milkPost[x_, list_]:=Join[x, {list[[(Length[list]+1)/2]]}]
Table[FromDigits[milk@IntegerDigits[i, 2], 2], {i, 0, 500}]
(*OR*)
Table[FromDigits[ResourceFunction["Shuffle"][IntegerDigits[i, 2], "Milk"], 2], {i, 0, 500}]
CROSSREFS
KEYWORD
AUTHOR
Sander G. Huisman, Nov 24 2020
STATUS
approved