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

1,2

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A245596, A073122, A256702.

Sequence in context: A366974 A346004 A195727 * A340714 A292381 A233655

Adjacent sequences: A256698 A256699 A256700 * A256702 A256703 A256704

Keyword

nonn,easy

Author

Clark Kimberling, Apr 09 2015

Status

approved