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A070123 Numbers m such that [A070080(m), A070081(m), A070082(m)] is an acute scalene integer triangle with prime side lengths. 8
240, 544, 799, 911, 1262, 1568, 2621, 2681, 2856, 3369, 3648, 4246, 5194, 5541, 6576, 6626, 6725, 7441, 7503, 7565, 7902, 7944, 8882, 8956, 9332, 9452, 9472, 9888, 9988, 10421, 10498, 10502, 11075, 11079, 11622 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..1778

Reinhard Zumkeller, Integer-sided triangles

EXAMPLE

240 is a term because: [A070080(240), A070081(240), A070082(240)]=[7<11<13], A070085(240)=7^2+11^2-13^2=49+121-169=1>0.

MATHEMATICA

m = 500 (* 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_} /; a < b < c && AllTrue[{a, b, c}, PrimeQ] && a^2 + b^2 - c^2 > 0] // Flatten (* Jean-François Alcover, Oct 12 2021 *)

CROSSREFS

Cf. A070097, A070118, A070111, A070112.

Sequence in context: A154378 A300145 A063372 * A119659 A263161 A268772

Adjacent sequences:  A070120 A070121 A070122 * A070124 A070125 A070126

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

STATUS

approved

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Last modified May 17 19:51 EDT 2022. Contains 353778 sequences. (Running on oeis4.)