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A240068
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Number of prime Lipschitz quaternions having norm prime(n).
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1
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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
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OFFSET
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1,1
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COMMENTS
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This sequence counts all prime Lipschitz quaternions having a given norm; A239394 counts only the prime nonnegative Lipschitz quaternions.
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LINKS
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FORMULA
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a(n) = 8 * (prime(n) + 1) = 8 * A008864(n).
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MATHEMATICA
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(* 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]
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CROSSREFS
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Cf. A055669 (number of prime Hurwitz quaternions of norm prime(n)).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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