OFFSET
1,41
COMMENTS
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.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..2586 (4-vectors)
Wikipedia , Hurwitz quaternion
EXAMPLE
The first six nonnegative prime Lipschitz quaternions are 1+i, 1+j, 1+k, i+j, i+k, and j+k.
MATHEMATICA
(* 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] &]
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
T. D. Noe, Mar 21 2014
STATUS
approved