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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
Sequence in context: A154378 A300145 A063372 * A119659 A263161 A268772
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2002
STATUS
approved

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Last modified May 21 22:16 EDT 2024. Contains 372741 sequences. (Running on oeis4.)