* Joerg Arndt <arndt@jjj.de> [Apr 08. 2014 13:28]:
* Joerg Arndt <arndt@jjj.de> [Apr 07. 2014 19:57]:
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WDS (personal email):
There's no way those OEIS sequences have anything to do with it, despite agreeing on your data.
Me: think again.
Because so many asked: The sequence(s) give the number of butterfly ops when a "splitting by factorization" is used. This is not stupid at all, because with it one can write a program to generate the routines. When other splitting schemes are allowed, lower op counts can sometimes be achieved. The (apparently) smallest example is for n=55, where the sequence term is 5, but 4 can be achieved using the splitting [ 27, 1, 27 ]. The n where I can improve start 55, 83, 85, 115, 128, 137, 255, 256, 257, ... That the powers of 2 (and nearby numbers) are there is a consequence of the 4 ops reversal of 63. The improvement for all n above is by just one step. Best, jj
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