The reason that the innermost terms (i.e., the factors in the product
indexed by p_5 in your output) are given as a recurrence rather than the
seemingly equivalent function f(p_5) = 1 is that they are in fact not
equivalent.
Yes, I understand this recurrence aspect.
The recurrence (p - 1) f(p) + p - 1 = 0 is satisfied also by f(0) = 1, f(1)
= 1783, f(2) = f(3) = 1:
guessRec([1,1783,1,1])
[[f(n): (- n + 1)f(n) + n - 1 = 0]]
In general, if you get such a result, it is very likely wrong, but we
cannot exclude the possibility that it is correct.
That raises the question, whether for the inner sequence you can do
something with initial values or do "arbitrary" values just appear and
are "summmed-away" by the possible outer sums?
A recurrence for the primes is of course a dream, but why does guess
gives me something for
guess([2,3,5,7,11,13])
and
guess([2,3,5,7,11,13,17,19])
but returns the empty list for guess([2,3,5,7,11,13,17])?
Is ist that you have not enough values to come up with the same formula
as with guess([2,3,5,7,11,13,17,19]) and one value too much to verify
that the formula for guess([2,3,5,7,11,13]) does not generate
[2,3,5,7,11,13,17]?
Still there is the question, how am I supposed to take the result apart
for further computation. That should be explained somewhere. You cannot
expect your users to know how the internals of Expression(Integer) are
to be handled.
Ralf
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