A260311 Difference sequence of A260317.

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

Offset

1,6

Comments

Conjecture: a(n) is a Fibonacci number (A000045) for every n.

In fact, a(n) is in {1,2,3,5}; proved with the Walnut theorem-prover. - Jeffrey Shallit, Oct 12 2022

Links

Table of n, a(n) for n=1..86.

The Walnut code at https://cs.uwaterloo.ca/~shallit/oeis-walnut.txt proves the conjecture.  Walnut itself can be downloaded from https://cs.uwaterloo.ca/~shallit/walnut.html.

Mathematica

r = GoldenRatio; z = 1060;
u[n_] := u[n] = Floor[n*r]; v[n_] := v[n] = Floor[n*r^2];
s[m_, n_] := v[m] + v[n];
t = Table[s[m, n], {n, 2, z}, {m, 1, n - 1}]; (* A259601 *)
w = Flatten[Table[Count[Flatten[t], n], {n, 1, z}]];
p0 = Flatten[Position[w, 0]]  (* A260317 *)
d = Differences[p0] (* A260311 *)

Crossrefs

Cf. A259556, A259600, A259601, A260317, A000045.

Sequence in context: A029424 A061498 A106029 * A188431 A105153 A000924

Adjacent sequences: A260308 A260309 A260310 * A260312 A260313 A260314

Keyword

nonn,easy

Author

Clark Kimberling, Jul 31 2015

Status

approved