A256660 Number of terms in the minimal alternating Fibonacci representation of n.

1, 1, 1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 2, 1, 3, 3, 2, 3, 2, 2, 2, 1, 3, 3, 3, 4, 2, 3, 3, 2, 3, 2, 2, 2, 1, 3, 3, 3, 4, 3, 4, 4, 2, 3, 3, 3, 4, 2, 3, 3, 2, 3, 2, 2, 2, 1, 3, 3, 3, 4, 3, 4, 4, 3, 5, 4, 4, 4, 2, 3, 3, 3, 4, 3, 4, 4, 2, 3, 3, 3, 4, 2, 3, 3, 2, 3

Offset: 0

Author

Clark Kimberling, Apr 08 2015

Keywords

• nonn
• easy

Comments

See A256655 for definitions.

Links

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

Crossrefs

Cf. A000045, A256655.

Programs

Mathematica

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[12];  r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]
t = Table[Length[r[n]], {n, 0, 120}]  (* A256660 *)