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, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 20 2024
STATUS
approved