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A070111
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Numbers k such that [A070080(k), A070081(k), A070082(k)] is an integer triangle with prime sides.
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9
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3, 5, 6, 9, 14, 16, 22, 30, 34, 35, 43, 46, 63, 84, 101, 109, 124, 133, 153, 159, 163, 170, 189, 193, 201, 234, 240, 286, 297, 328, 334, 350, 352, 382, 392, 410, 444, 450, 454, 472, 478, 479, 515, 519, 527, 542, 544, 597, 603, 621, 629, 688, 708, 714, 771, 777, 795, 799, 811, 817, 868, 878, 900, 907, 911
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..65.
Reinhard Zumkeller, Integer-sided triangles
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EXAMPLE
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35 is a term: [A070080(35), A070081(35), A070082(35)]=[2,7,7].
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MATHEMATICA
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m = 50 (* max perimeter *);
sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1] & // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
Position[triangles, {a_, b_, c_} /; AllTrue[{a, b, c}, PrimeQ]] // Flatten (* Jean-François Alcover, Oct 04 2021 *)
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CROSSREFS
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Cf. A070088, A070114, A070117, A070120, A070123, A070126, A070129, A070132, A070135.
Sequence in context: A075472 A072522 A294909 * A070117 A176345 A101139
Adjacent sequences: A070108 A070109 A070110 * A070112 A070113 A070114
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, May 05 2002
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EXTENSIONS
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More terms from Jean-François Alcover, Oct 04 2021
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STATUS
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approved
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