# Witt transform examples in the OEIS

Richard Mathar mathar at strw.leidenuniv.nl
Thu Jul 31 20:49:14 CEST 2008

```SeqFans,

today a big effort to create one new sequence started: The new round of Al Zimmermann's Programming Contest.

The task is to find n-tuples of integers a_i, such that there are as
many distinct primes as possible among the 3^n sums a_i*c_i, where the
coeffcients c_i may assume any of the 3 values -1,0,1.

Example: The 4 numbers "10 29 82 106" produce 9 distinct primes:

5 = 106 + 10 - 82 - 29
19 = 29 - 10
29 = 29
43 = 82 - 29 - 10
53 = 82 - 29
67 = 106 - 29 - 10
101 = 82 + 29 - 10
149 = 106 + 82 - 29 -10
227 = 106 + 82 + 29 + 10

At the end of the contest, which will be on Nov 10, 2008, we might have a new sequence "Maximum number of distinct primes among all 3^n possible sums that can be made from n signed addends, using each addend at most once".
I would appreciate, if someone with better knowledge of English mathematical language could correct or improve this deficient proposal.

The (future) sequence will start

1 4 9 27 ... a(5)>=71
a(2)=4 can be made by 2 and 5 as sum terms, because 2, 3=5-2, 5, 7=5+2
Since the contest addresses the range n=3,...,14 please don't explain here why a(3)=9 or a(4)=27. Anything beyond a(4) seems rather hard to find.

If you think the problem is interesting, you should consider to participate in the contest yourself. The web page is at
http://www.recmath.org/contest/index.php

The detailed description can be found at
http://www.recmath.org/contest/description.php

Hugo Pfoertner

```