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A378242
Lexicographically earliest sequence of nonnegative integers such that each term does not belong to a Fibonacci-like sequence starting with two earlier terms.
3
0, 1, 4, 6, 11, 19, 24, 27, 29, 36, 50, 66, 71, 92, 105, 112, 114, 117, 122, 140, 154, 170, 179, 186, 196, 201, 218, 249, 265, 277, 297, 325, 328, 381, 386, 407, 441, 446, 449, 459, 469, 471, 481, 501, 513, 523, 544, 592, 607, 614, 624, 681, 701, 715, 753, 775
OFFSET
1,3
COMMENTS
In other words, for any n > 0, a(n) is as small as possible so as not to belong to a sequence F defined by F(0) = a(i), F(1) = a(j) for some i, j < n, and then F(k+2) = F(k) + F(k+1).
By necessity, the sequence is strictly increasing.
LINKS
Rémy Sigrist, C++ program
EXAMPLE
We can take a(1) = 0, as the first term is only required to be nonnegative.
We cannot take a(2) = 0, as 0 belongs to the Fibonacci-like sequence starting with 0 and 0.
We can take a(2) = 1.
From now on, we can no longer choose a Fibonacci number.
We can take a(3) = 4, the first nonnegative number that is not a Fibonacci number.
PROG
(C++) // See Links section.
CROSSREFS
Sequence in context: A197985 A058579 A022318 * A291916 A047811 A244010
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 20 2024
STATUS
approved