Addition chains: Difference between revisions
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For each n in {7,14,21,29,32,42,64} display the following : l(n), the count of Brauer chains of length l(n), an example of such a Brauser chain, the count of non-brauer chains of length l(n), an example of such a chain. (NB: counts may be 0 ). |
For each n in {7,14,21,29,32,42,64} display the following : l(n), the count of Brauer chains of length l(n), an example of such a Brauser chain, the count of non-brauer chains of length l(n), an example of such a chain. (NB: counts may be 0 ). |
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Extra-credit: Same task for n in {47,79,379, 12509} |
Extra-credit: Same task for n in {47, 79, 191, 382 , 379, 12509} |
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'''References''' |
'''References''' |
Revision as of 18:29, 28 January 2016
Addition chains is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
An addition chain of length r for n is a sequence 1 = a(0) < a(1) < a(2) ... < a(r) = n , such as a(k) = a(i) + a(j) ( i < k and j < k , i may be = j) . Each member is the sum of two earlier members, not necessarily distincts.
A Brauer chain for n is an addition chain where a(k) = a(k-1) + a(j) with j < k. Each member uses the previous member as a summand.
We are interested in chains of minimal length l(n).
Task
For each n in {7,14,21,29,32,42,64} display the following : l(n), the count of Brauer chains of length l(n), an example of such a Brauser chain, the count of non-brauer chains of length l(n), an example of such a chain. (NB: counts may be 0 ).
Extra-credit: Same task for n in {47, 79, 191, 382 , 379, 12509}
References
- OEIS sequences A079301, A079302. [1]
- Richard K. Guy - Unsolved problems in Number Theory - C6 - Addition chains.
Example
- minimal chain length l(19) = 6
- brauer-chains(19) : count = 31 Ex: #( 1 2 3 4 8 11 19)
- non-brauer-chains(19) : count = 2 Ex: #( 1 2 3 6 7 12 19)