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

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, 34, 36, 32, 33, 32, 32, 32, 65, 66, 68, 68, 73, 72, 72, 72, 81, 82, 84, 80, 81, 80, 80, 64, 65, 66, 68, 68, 73, 72, 72, 64, 65, 66, 68, 64, 65, 64, 64, 64, 129, 130

Offset: 1

Author

Clark Kimberling, Apr 09 2015

Keywords

• nonn
• easy

Examples

			R(1) = 1; positive part 1, nonpositive part 0
R(2) = 2; positive part 2, nonpositive part 0
R(3) = 4 - 1; positive part 4, nonpositive part 1
R(11) = 16 - 8 + 4 - 1; positive part 16+4 = 20; nonpositive part 8 + 1 = 9
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A245596, A073122, A256702.

Programs

Mathematica

b[n_] := 2^n; bb = Table[b[n], {n, 0, 40}];
s[n_] := Table[b[n + 1], {k, 1, b[n]}];
h[0] = {1}; h[n_] := Join[h[n - 1], s[n - 1]];
g = h[10]; Take[g, 100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]
Table[Total[Abs[r[n]]], {n, 1, 100}] (* A073122 *)
u = Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 100}]  (* A256701 *)
v = Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 100}]  (* A256702 *)

Formula

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