A070111 Numbers k such that [A070080(k), A070081(k), A070082(k)] is an integer triangle with prime sides.

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

Offset

1,1

Links

Table of n, a(n) for n=1..65.

Reinhard Zumkeller, Integer-sided triangles

Example

35 is a term: [A070080(35), A070081(35), A070082(35)]=[2,7,7].

Mathematica

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 *)

Crossrefs

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

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Extensions

More terms from Jean-François Alcover, Oct 04 2021

Status

approved