Infinite Sequence
There are infinitely many Ulam numbers. For, after the first n numbers in the sequence have already been determined, it is always possible to extend the sequence by one more element: Un − 1 + Un is uniquely represented as a sum of two of the first n numbers, and there may be other smaller numbers that are also uniquely represented in this way, so the next element can be chosen as the smallest of these uniquely representable numbers.
Ulam is said to have conjectured that the numbers have zero density, but they seem to have a density of approximately 0.07396.
Read more about this topic: Ulam Number
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