A256701 - OEIS

%I #4 Apr 13 2015 09:40:21

%S 1,2,4,4,9,8,8,8,17,18,20,16,17,16,16,16,33,34,36,36,41,40,40,32,33,

%T 34,36,32,33,32,32,32,65,66,68,68,73,72,72,72,81,82,84,80,81,80,80,64,

%U 65,66,68,68,73,72,72,64,65,66,68,64,65,64,64,64,129,130

%N Positive part of the minimal alternating binary representation of n (defined at A245596).

%H Clark Kimberling, <a href="/A256701/b256701.txt">Table of n, a(n) for n = 1..1000</a>

%F A256701(n) - A256702(n)  = n.

%e R(1) = 1; positive part 1, nonpositive part 0

%e R(2) = 2; positive part 2, nonpositive part 0

%e R(3) = 4 - 1; positive part 4, nonpositive part 1

%e R(11) = 16 - 8 + 4 - 1; positive part 16+4 = 20; nonpositive part 8 + 1 = 9

%t b[n_] := 2^n; bb = Table[b[n], {n, 0, 40}];

%t s[n_] := Table[b[n + 1], {k, 1, b[n]}];

%t h[0] = {1}; h[n_] := Join[h[n - 1], s[n - 1]];

%t g = h[10]; Take[g, 100]; r[0] = {0};

%t r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]

%t Table[Total[Abs[r[n]]], {n, 1, 100}] (* A073122 *)

%t u = Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 100}]  (* A256701 *)

%t v = Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 100}]  (* A256702 *)

%Y Cf. A245596, A073122, A256702.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Apr 09 2015