[seqfan] Re: sequence defined by ``exotic addition''

Maximilian Hasler maximilian.hasler at gmail.com
Tue Dec 22 17:17:51 CET 2009

```> 1/
> Note that the 1st component of n x [1,1] is given in A087808.

sorry, this was wrong, I computed the sequence incorrectly...
OTOH, correcting my code to conform to your definition :
>> 2n x a = (n x a) o (n x a)
>> 2n+1 x a= ((n x a) o (n x a)) o a
>> 1 x a = a

i.e.
r(a,b)=[a[1]+b[1],a[1]*b[2]+a[2]*b[1]]
gg(n,a=[1,1])=if(n%2,n==1&return(a);r(gg(n-1,a),a),a=gg(n\2,a);r(a,a))

I get  (n x [1,1])[1] = n
(as should be expected, since 1st component is normal addition)
but for the 2nd component another sequence than that given in your o.p.

vector(99,i,gg(i,[1,1])[2])
[1, 2, 4, 8, 12, 24, 30, 64, 72, 120, 130, 288, 300, 420, 434, 1024,
1040, 1296, 1314, 2400, 2420, 2860, 2882, 6912, 6936, 7800, 7826,
11760, 11788, 13020, 13050, 32768, 32800, 35360, 35394, 46656, 46692,
49932, 49970, 96000, 96040, 101640, 101682, 125840,...]

and not

>> 1,2,4,8,12,24,40,64,72,144,224,320,416,576,768,1024,1040 ...

Maximilian

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