OFFSET
1,1
COMMENTS
The vectors are multiplied by 2 because a Hurwitz quaternion can have half-integer 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.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..2612 (4-vectors)
Wikipedia, Hurwitz quaternion.
MATHEMATICA
(* first << Quaternions` *) mx = 5; lst = Flatten[Table[{a, b, c, d}/2, {a, 0, mx}, {b, 0, mx}, {c, 0, mx}, {d, 0, mx}], 3]; q = Select[lst, Norm[Quaternion @@ #] < mx^2 && PrimeQ[Quaternion @@ #, Quaternions -> True] &]; 2*Sort[q, Norm[#1] < Norm[#2] &]
CROSSREFS
KEYWORD
nonn,nice,tabf
AUTHOR
T. D. Noe, Mar 21 2014
STATUS
approved