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

Author

Clark Kimberling, Apr 01 2020

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Crossrefs

Cf. A003622, A035513, A333309.

Programs

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 *)