Sanity Check

wouter meeussen wouter.meeussen at
Sat Oct 19 19:04:33 CEST 2002

superseeker came up empty on:
1, 2, 3, 6, 11, 20, 53, 130, 196, 725, 1990
(once with 10 terms, and again with 8)

Start with 2n-bead black-white reversible complementable necklaces
with n black beads (=A006840),
replace the white beads by unit vectors (roots of unity) pointing
to them,
and then count only those with a different vector sum.

(equivalent to number of different sums produced by n different
roots of unity choosen from E^(-k I Pi/(2n)), k=[1..2n] ??)

but this would then be:
ID Number: A004135 (Formerly M0782) Sequence:
1,2,3,6,11,19,28,40,56,72,96,114,147,178 Name: Additive bases:
a(n) is the least integer k such that in the cyclic group Z_k
there is a subset of n elements all pairs (of distinct elements)
of which add up to a different sum (in Z_k).

weird, not really 'clean'!
Sanity Check, anyone?

Wouter Meeussen
wouter.meeussen at

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