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A256701 Positive part of the minimal alternating binary representation of n (defined at A245596).

%I A256701 #4 Apr 13 2015 09:40:21
%S A256701 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 A256701 34,36,32,33,32,32,32,65,66,68,68,73,72,72,72,81,82,84,80,81,80,80,64,
%U A256701 65,66,68,68,73,72,72,64,65,66,68,64,65,64,64,64,129,130
%N A256701 Positive part of the minimal alternating binary representation of n (defined at A245596).
%H A256701 Clark Kimberling, <a href="/A256701/b256701.txt">Table of n, a(n) for n = 1..1000</a>
%F A256701 A256701(n) - A256702(n)  = n.
%e A256701 R(1) = 1; positive part 1, nonpositive part 0
%e A256701 R(2) = 2; positive part 2, nonpositive part 0
%e A256701 R(3) = 4 - 1; positive part 4, nonpositive part 1
%e A256701 R(11) = 16 - 8 + 4 - 1; positive part 16+4 = 20; nonpositive part 8 + 1 = 9
%t A256701 b[n_] := 2^n; bb = Table[b[n], {n, 0, 40}];
%t A256701 s[n_] := Table[b[n + 1], {k, 1, b[n]}];
%t A256701 h[0] = {1}; h[n_] := Join[h[n - 1], s[n - 1]];
%t A256701 g = h[10]; Take[g, 100]; r[0] = {0};
%t A256701 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]
%t A256701 Table[Total[Abs[r[n]]], {n, 1, 100}] (* A073122 *)
%t A256701 u = Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 100}]  (* A256701 *)
%t A256701 v = Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 100}]  (* A256702 *)
%Y A256701 Cf. A245596, A073122, A256702.
%K A256701 nonn,easy
%O A256701 1,2
%A A256701 _Clark Kimberling_, Apr 09 2015