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Addition Chain

An addition chain for a number n is a sequence 1=a_0<a_1<...<a_r=n, such that each member after a_0 is the sum of two earlier (not necessarily distinct) ones. The number r is called the length of the addition chain. For example,

1,1+1=2,2+2=4,4+2=6,6+2=8,8+6=14

is an addition chain for 14 of length r=5 (Guy 1994).

See also

Brauer Chain, Hansen Chain, Scholz Conjecture

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References

Guy, R. K. "Addition Chains. Brauer Chains. Hansen Chains." §C6 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 111-113, 1994.

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Addition Chain

Cite this as:

Weisstein, Eric W. "Addition Chain." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AdditionChain.html

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