[seqfan] computability of A080075 Proth numbers

[Georgi Guninski]

A080075 Proth numbers: of the form k*2^m + 1 for k odd, m >= 1 and 2^m >
k

machine analysis seems to suggest these relations (verified to 10 000
against the OEIS bfile)

a(2*n-1) = (4*a(n - 1) - 3)
a(2*n) = ( 2*a(n - 1) + 2*a(n) - 3 )
a(2*n+1) = (4*a(n) - 3)

a(n+1) = (-a(n - 1) + 2*a(n))

OR (these are the roots of a quadratic relation, a possible approach may
be to take the smaller proth of them)

a(n+1) = (-2*a(n - 1) + 3*a(n))

doubling formulas resemble "divide and conquer sequences" - do proth
numbers have generating function ?

-- 
joro