A256702 Nonpositive part of the minimal alternating binary representation of n (defined at A256696).

0, 0, 1, 0, 4, 2, 1, 0, 8, 8, 9, 4, 4, 2, 1, 0, 16, 16, 17, 16, 20, 18, 17, 8, 8, 8, 9, 4, 4, 2, 1, 0, 32, 32, 33, 32, 36, 34, 33, 32, 40, 40, 41, 36, 36, 34, 33, 16, 16, 16, 17, 16, 20, 18, 17, 8, 8, 8, 9, 4, 4, 2, 1, 0, 64, 64, 65, 64, 68, 66, 65, 64, 72

Offset

1,5

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. A256696, A073122, A256701.

Sequence in context: A325146 A195152 A085668 * A266921 A248721 A110324

Adjacent sequences: A256699 A256700 A256701 * A256703 A256704 A256705

Keyword

nonn,easy

Author

Clark Kimberling, Apr 09 2015

Status

approved