A240068 Number of prime Lipschitz quaternions having norm prime(n).

24, 32, 48, 64, 96, 112, 144, 160, 192, 240, 256, 304, 336, 352, 384, 432, 480, 496, 544, 576, 592, 640, 672, 720, 784, 816, 832, 864, 880, 912, 1024, 1056, 1104, 1120, 1200, 1216, 1264, 1312, 1344, 1392, 1440, 1456, 1536, 1552, 1584, 1600, 1696, 1792

Offset

1,1

Comments

This sequence counts all prime Lipschitz quaternions having a given norm; A239394 counts only the prime nonnegative Lipschitz quaternions.

Links

Table of n, a(n) for n=1..48.

Wikipedia, Hurwitz quaternion

Formula

a(n) = 8 * (prime(n) + 1) = 8 * A008864(n).

Mathematica

(* first << Quaternions` *)
mx = 17; lst = Flatten[Table[{a, b, c, d}, {a, -mx, mx}, {b, -mx, mx}, {c, -mx, mx}, {d, -mx, 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), A239394.

Cf. A055669 (number of prime Hurwitz quaternions of norm prime(n)).

Sequence in context: A102374 A364353 A317534 * A269424 A319928 A025102

Adjacent sequences: A240065 A240066 A240067 * A240069 A240070 A240071

Keyword

nonn

Author

T. D. Noe, Apr 01 2014

Status

approved