Problem 45250. Be happy

Hi Asif: Can you give a little more detail to your solvers about what "happy" and "b-base' mean? Maybe link to Wikipedia reference pages?

https://en.wikipedia.org/wiki/Happy_number

Asif: If I am reading that reference correctly, then test suite problems 4 and 7 are incorrect. In fact, problem 4 has base b=4, and according to the reference b=4 is a "happy base" in which *all* numbers are happy.

thank u william for pointing that out.
i've modified the test suites.
kindly inform if u find any more discrepancies.

Asif: Yes, I am now seeing a discrepancy with problem 6, but all the others agree with my code.

william, so far i've understood the concept, test-6 is correct.
https://en.wikipedia.org/wiki/Perfect_digital_invariant
have a look..I think it'll make things clear
but still if i'm wrong,do inform

Well, it appears to me that the number 742356 is a pre-periodic point of the perfect digital invariant n=8 in base 3. However, since the perfect digital invariant is n=8 rather than n=1, this is not a happy number. At least, that is how I read it!

william
did u look into the nontrivial PDI portion?
i might have been wrong-i 'll look into it when i get some time. i'm a bit busy now with my new job

Asif, Yes, I looked at the information on non-trivial perfect digital invariants. Near the end of that reference, there is a short section entitled "Relation to happy numbers" that indicates that in order for a number to be happy, it needs to be a perfect digital invariant with the value of 1. In this case, the invariant is 8 (or 22 in base-3), so I interprete that as saying that it is a non-trivial PDI, but not happy.