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A167654 Simple zero-divisors of Cayley-Dickson algebras 0

%I

%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.

%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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Last modified May 16 05:02 EDT 2022. Contains 353690 sequences. (Running on oeis4.)