%I #10 Mar 22 2014 13:01:29
%S 1,1,0,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,1,1,0,1,1,0,
%T 1,1,0,1,1,1,2,1,0,0,2,0,1,0,2,0,0,1,1,2,0,0,1,0,2,0,1,0,0,2,0,2,1,0,
%U 0,2,0,1,0,1,2,0,0,1,0,2,0,0,2,1,0,0,1,2
%N Nonnegative prime Lipschitz quaternions shown as 4-vectors sorted by norm and then (1,i,j,k) components.
%C A Lipschitz quaternion has all integer components. The norms of quaternions are (rational) primes 2, 3, 5, 7, 11,... A quaternion is commonly written a + b*i + c*j + d*k, where 1, i, j, and k are units.
%H T. D. Noe, <a href="/A239393/b239393.txt">Table of n, a(n) for n = 1..2586</a> (4-vectors)
%H Wikipedia , <a href="http://en.wikipedia.org/wiki/Hurwitz_quaternion">Hurwitz quaternion</a>
%e The first six nonnegative prime Lipschitz quaternions are 1+i, 1+j, 1+k, i+j, i+k, and j+k.
%t (* first << Quaternions` *) mx = 5; lst = Flatten[Table[{a, b, c, d}, {a, 0, mx}, {b, 0, mx}, {c, 0, mx}, {d, 0, mx}], 3]; q = Select[lst, Norm[Quaternion @@ #] < mx^2 && PrimeQ[Quaternion @@ #, Quaternions -> True] &]; Sort[q, Norm[#1] < Norm[#2] &]
%Y Cf. A239394 (number of Lipschitz quaternions having norm prime(n)).
%Y Cf. A239395 (Hurwitz quaternions).
%K nonn,nice
%O 1,41
%A _T. D. Noe_, Mar 21 2014
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