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A070111 Numbers k such that [A070080(k), A070081(k), A070082(k)] is an integer triangle with prime sides. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)