x->2x+1 map while x is squarefree

[zak seidov]

Seqfans,
what is the longest sequence of squarefree numbers
n*2^i-1, i=1,2,...?
E.g. starting with n=2, the sequence has 13 terms:
2,5,11,23,47,95,191,383,767,1535,3071,6143,12287,
and next number 24575 is not squarefree.
Up to n=2000, the longest sequence with 95 terms
is for n=1574.
Thanks, Zak 

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