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Encyclopedia > Addition chain

In mathematics, an addition chain is a sequence a0, a1, a2, a3, ... that satisfies

a0 = 1, and
for each k>0: ak = ai + aj for some i, j < k.

As an example: 1, 2, 3, 6, 12, 24, 30, 31 is an addition chain for 31, of length 7, since

2 = 1 + 1
3 = 2 + 1
6 = 3 + 3
12 = 6 + 6
24 = 12 + 12
30 = 24 + 6
31 = 30 + 1

Addition chains can be used for exponentiation: so for example we only need 7 multiplications to calculate 531:

52 = 51 51
53 = 52 51
56 = 53 53
512 = 56 56
524 = 512 512
530 = 524 56
531 = 530 51

See also:

External links

  • http://wwwhomes.uni-bielefeld.de/achim/addition_chain.html

  Results from FactBites:
 
NationMaster - Encyclopedia: Addition chain (218 words)
In mathematics, an addition chain is a sequence a
Addition chains can be used for exponentiation: so for example we only need 7 multiplications to calculate 5
In mathematics, addition chain exponentiation is a fast method of exponentation.
Chapter 16. Polymers. Characteristics, Applications and Processing (792 words)
Elastic elongation is due to uncoiling, untwisting and straightening of chains in the stress direction.
In vulcanization, crosslinking of the elastomeric polymer is achieved by an irreversible chemical reaction usually at high temperatures (hence ‘vulcan’), and usually involving the addition of sulfur compounds.
In silicone rubbers, the backbone C atoms are replaced by a chain of alternating silicon and oxygen atoms.
  More results at FactBites »


 
 

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