A239396 Number of prime nonnegative Hurwitz quaternions having norm prime(n).

6, 8, 18, 12, 24, 30, 42, 36, 36, 66, 48, 66, 90, 72, 72, 102, 108, 114, 108, 108, 126, 120, 144, 174, 162, 198, 156, 180, 186, 198, 192, 228, 234, 228, 270, 228, 258, 252, 252, 306, 300, 306, 288, 306, 330, 300, 336, 336, 372, 378, 390, 360, 402, 420, 438

Offset

1,1

Comments

For n > 1, there are prime(n) + 1 more nonnegative Hurwitz quaternions than nonnegative Lipschitz quaternions. - T. D. Noe, Mar 31 2014

Links

Table of n, a(n) for n=1..55.

Wikipedia, Hurwitz quaternion

Example

The six prime nonnegative Hurwitz quaternions having norm 2 are 1+i, 1+j, 1+k, i+j, i+k, and j+k.

Mathematica

(* first << Quaternions` *) mx = 17; 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] &]; q2 = Sort[q, Norm[#1] < Norm[#2] &]; Take[Transpose[Tally[(Norm /@ q2)^2]][[2]], mx]

Crossrefs

Cf. A239393 (prime Lipschitz quaternions).

Cf. A239395 (prime Hurwitz quaternions).

Sequence in context: A112158 A270046 A093479 * A340519 A315942 A315943

Adjacent sequences: A239393 A239394 A239395 * A239397 A239398 A239399

Keyword

nonn

Author

T. D. Noe, Mar 21 2014

Status

approved