Addition Chain

In mathematics, an addition chain for computing a positive integer n can be given by a sequence of natural numbers v and a sequence of index pairs w such that each term in v is the sum of two previous terms, the indices of those terms being specified by w:

v =(v0,...,vs), with v0 = 1 and vs = n
for each 0< is holds: vi = vj + vk, with wi=(j,k) and 0 ≤ j,ki − 1

Often only v is given since it is easy to extract w from v, but sometimes w is not uniquely reconstructible. An introduction is given by Knuth.

Read more about Addition Chain:  Examples, Methods For Computing Addition Chains, Chain Length, Brauer Chain, Scholz Conjecture

Famous quotes containing the words addition and/or chain:

    Napoleon wanted to turn Paris into Rome under the Caesars, only with louder music and more marble. And it was done. His architects gave him the Arc de Triomphe and the Madeleine. His nephew Napoleon III wanted to turn Paris into Rome with Versailles piled on top, and it was done. His architects gave him the Paris Opera, an addition to the Louvre, and miles of new boulevards.
    Tom Wolfe (b. 1931)

    To avoid tripping on the chain of the past, you have to pick it up and wind it about you.
    Mason Cooley (b. 1927)