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.
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. All the best, Martin On Tuesday, 23 August 2022 at 17:22:01 UTC+2 Waldek Hebisch wrote: > On Tue, Aug 23, 2022 at 04:26:02PM +0200, Ralf Hemmecke wrote: > > Martin, Waldek, > > > > can you tell me how I am supposed to interpret the result of this: > > > > (153) -> guess([2,3,5,7,11,13,17,19]) > > > > (153) > > [ > > s - 1 p - 1 s - 1 > > n - 1 8 7 6 > > --+ ++-++ --+ ++-++ > > > | | > - | | [f(p ): (p - 1)f(p ) + p - 1 = 0] > > + 2 > > --+ | | --+ | | 5 5 5 5 > > s = 0 p = 0 s = 0 p = 0 > > 8 7 6 5 > > + > > 2 > > ] > > > > Martin can probably give better explanation, but I will try. 'guess' > tries to represent seqence as sums or product of simpler sequence > and is doing this recursivly. So we have sum of products of sums > of producs where inner term is f(p_5) and f satifies given > equation. There is display problem: first 2 is added to inner sum > (so we really should have parentheses around inner sum + 2). > Scalar term should be put before sum (but unfortunately current > diplay logic puts them last creating extra confusion). > > Also, equation defines rational function. Looking at InputForm > I see that this is reccurence equation of order 0. 'guess' > probably should simplify this to rational function (in this case > constant 1). > > Of course, as ususal there is trouble if we have enough data > to support out guess. Funnily, if I add next prime I get > the same formula, so it passes normal sanity check. > > -- > Waldek Hebisch > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/90f7aea4-2918-4fa7-8177-4be2244ed00en%40googlegroups.com.
