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 A240068 Number of prime Lipschitz quaternions having norm prime(n). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 21 03:36 EDT 2024. Contains 371850 sequences. (Running on oeis4.)