Mersenne numbers and the (divisors) property.

[alexandre.wajnberg at skynet.be]

Le mercredi, 27 avr 2005, à 15:52 Europe/Brussels, Gerald McGarvey a  
écrit :
> Something to note about A007733:
> For 2 <= n <= 84, A000010(n) / A007733(n) results in the following  
> sequence
> 1 1 2 1 1 2 4 1 1 1 2 1 2 2 8 2 1 1 2 2 1 2 4 1 1 1 4 1 2 6 16 2 2 2 2  
> 1 ...
> and it seems reasonable to conjecture that A007733 always divides  
> A000010
> http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/ 
> eisA.cgi?Anum=A000010
> -- Gerald



Another thing to note (I don't know if it's of interest for your  
discussion) is that A007733 is a fractal sequence, related to A002326:

A007733:  
1,1,2,1,4,2,3,1,6,4,10,2,12,3,4,1,8,6,18,4,6,10,11,2,20,12,18,3,28,4,5,1 
,10,8,12,6,36,18,12,4,20,6,14,10,12,11,23,2,21,20,8,12,52,18,20,3,18,28, 
58,4,60,5,6,1,12,10,66,8,22,12,35, 6,9,36,20,18,30,12,39,4,54,20,82,6

The even-index terms of this sequence are this sequence itself,  
constructed on A002326, whose terms are the odd-index terms of this  
sequence.

Alexandre
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