A272215 a(n) = that number formed by permuting the digits of n which is divisible by the highest power of 2 (in case of a tie, choose the smallest number).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 12, 22, 32, 24, 52, 26, 72, 28, 92, 30, 13, 32, 33, 34, 35, 36, 37, 38, 39, 40, 14, 24, 34, 44, 54, 64, 74, 48, 94, 50, 15, 52, 35, 54, 55, 56, 57, 58, 59, 60, 16, 26, 36, 64, 56, 66, 76, 68, 96, 70, 17, 72, 37, 74, 57, 76, 77, 78, 79, 80, 18, 28, 38

Offset

1,2

Comments

There is no reason to allow permutations that begin with 0, because we can always gain a power of 2 by putting that zero at the other end. - N. J. A. Sloane, Apr 23 2016

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

The numbers obtained by permuting the digits of 1336 are 1336, 1363, 1633, 3136, 3163, 6133, 3316, 3613, 6313, 3361, 3631 and 6331. The highest power of 2 dividing any of these is 2^6, which divides just one of them, 3136, so a(1336) = 3136.

Mathematica

hp2[n_]:=Module[{c={#, IntegerExponent[#, 2]}&/@(FromDigits/@ Permutations[ IntegerDigits[ n]]), mx}, mx=Max[c[[All, 2]]]; Min[Select[c, #[[2]]==mx&][[All, 1]]]]; Array[hp2, 90] (* Harvey P. Dale, Jan 27 2020 *)

Crossrefs

Cf. A261370, A272216.

Sequence in context: A348287 A328447 A107602 * A323366 A030066 A355479

Adjacent sequences: A272212 A272213 A272214 * A272216 A272217 A272218

Keyword

nonn,base,look

Author

David A. Corneth, Apr 22 2016

Status

approved