A333308 Numbers that are the sum of two distinct terms of A003622 (1st column of the Wythoff array, A035513).

5, 7, 10, 13, 15, 16, 18, 20, 21, 23, 25, 26, 28, 29, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 54, 55, 57, 58, 59, 60, 62, 63, 65, 67, 68, 70, 71, 72, 73, 75, 76, 78, 79, 80, 81, 83, 84, 86, 88, 89, 91, 92, 93, 94, 96, 97, 99, 100, 101

Offset

1,1

Comments

Conjecture: the difference sequences of this sequence and its complement consist exclusively of Fibonacci numbers (A000045).

Links

Table of n, a(n) for n=1..64.

Example

A003622 = {1,4,6,9,12,14,17,19,22,25,...}, so that sums of two distinct terms are
1+4 = 5, 1+6 = 7, 4+6 = 10, 1+9 = 10, 4+9 = 13, 6+9 = 15, ...  Delete duplicates (such as 10) and arrange the resulting sums in increasing order.

Mathematica

w[n_] := Floor[n*GoldenRatio] + n - 1; (* A003622 *)
s[n_] := Table[w[n] + w[k], {k, 1, n - 1}];
t = Table[s[n], {n, 1, 200}]; u = Union[Flatten[t]]  (* A333308 *)
v = Complement[Range[Max[u]], u]  (* A333309 *)

Crossrefs

Cf. A003622, A035513, A333309.

Sequence in context: A154689 A175766 A243187 * A179196 A024325 A060873

Adjacent sequences: A333305 A333306 A333307 * A333309 A333310 A333311

Keyword

nonn,easy

Author

Clark Kimberling, Apr 01 2020

Status

approved