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%I #12 Dec 31 2023 04:29:47
%S 0,0,0,0,42,294,1518,6942,29886
%N Simple zero-divisors of Cayley-Dickson algebras
%C Zero divisors of the form e+f where e and f are units of the Cayley-Dickson algebra with 2^n elements.
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a> section 39.14.4 "Simple zero-divisors of the sedenions", p.820-821.
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/demo/arith/#zero-divisors">List</a> of simple zero-divisors of the sedenions.
%e There are no zero-divisors for reals (n=0), complex numbers (n==1), quaternions (n=2), and octonions (n=3). For the sedenions there are 42 sums of two units that are zero divisors. For example ( 1 + 10 ) * ( 5 + 14 ) is zero, so (1+10) is a simple zero divisor (writing k for the k-th unit, starting with 0).
%K more,nonn
%O 0,5
%A _Joerg Arndt_, Nov 08 2009
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