Vectorial Addition Chain - Addition Sequence

An addition sequence for the set of integer S ={n0, ...,nr-1} is an addition chain v that contains every element of S.

For example, an addition sequence computing

{47,117,343,499}

is

(1,2,4,8,10,11,18,36,47,55,91,109,117,226,343,434,489,499).

It's possible to find addition sequence from vectorial addition chains and vice versa, so they are in a sense dual.

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