| Popis: |
An Ulam sequence U ( a , b ) is defined as a sequence starting with integers a , b such that 0 a b , and such that every subsequent term is the smallest integer that can be written as the sum of distinct previous terms in exactly one way. We investigate a new rigidity phenomenon for families U ( a , b ) , where a is fixed and we allow b to increase, centering around a result proved using a novel model theoretic argument. For the specific case U ( 1 , n ) , we provide an algorithm for computing relevant coefficients, together with a proof of correctness. |
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