A256662 -id:A256662 - cp's OEIS frontend

A256663 Nonnegative part of the minimal alternating Fibonacci representation of n.

0, 1, 2, 3, 5, 5, 8, 8, 8, 14, 13, 13, 13, 13, 22, 23, 21, 22, 21, 21, 21, 21, 35, 36, 37, 39, 34, 35, 36, 34, 35, 34, 34, 34, 34, 56, 57, 58, 60, 60, 63, 63, 55, 56, 57, 58, 60, 55, 56, 57, 55, 56, 55, 55, 55, 55, 90, 91, 92, 94, 94, 97, 97, 97, 103, 102

Offset: 0

Clark Kimberling, Apr 08 2015

See A256655 for definitions.

			R(9) = 13 - 5 + 1, so that a(9) = 13 + 1 = 14.

Clark Kimberling, Table of n, a(n) for n = 0..1000

Cf. A000045, A256655, A256662, A256664.

b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
g = h[23];
r[0] = {0}; r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[Total[Abs[r[n]]], {n, 0, 100}] (* A256662 *)
Table[Total[(Abs[r[n]] + r[n])/2], {n, 0, 100}]  (* A256663 *)
Table[Total[(Abs[r[n]] - r[n])/2], {n, 0, 100}]  (* A256664 *)

A256663(n) - A256664(n) = n.

A256664 Nonpositive part of the minimal alternating Fibonacci representation of n.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 2, 1, 0, 5, 3, 2, 1, 0, 8, 8, 5, 5, 3, 2, 1, 0, 13, 13, 13, 14, 8, 8, 8, 5, 5, 3, 2, 1, 0, 21, 21, 21, 22, 21, 23, 22, 13, 13, 13, 13, 14, 8, 8, 8, 5, 5, 3, 2, 1, 0, 34, 34, 34, 35, 34, 36, 35, 34, 39, 37, 36, 35, 21, 21, 21, 21, 22, 21, 23

Offset: 0

Clark Kimberling, Apr 08 2015

See A256655 for definitions.

			R(9) = 13 - 5 + 1, so that a(9) = 5.

Clark Kimberling, Table of n, a(n) for n = 0..1000

Cf. A000045, A256655, A256662, A256663.

b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
g = h[23];  r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[Total[Abs[r[n]]], {n, 0, 100}] (* A256662 *)
Table[Total[(Abs[r[n]] + r[n])/2], {n, 0, 100}]  (* A256663 *)
Table[Total[(Abs[r[n]] - r[n])/2], {n, 0, 100}]  (* A256664 *)

A256663(n) - A256664(n) = n.

cp's OEIS Frontend

A256663 Nonnegative part of the minimal alternating Fibonacci representation of n.

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