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A333308
Numbers that are the sum of two distinct terms of A003622 (1st column of the Wythoff array, A035513).
2
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).
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 01 2020
STATUS
approved