A070112 - OEIS

A070112

Numbers n such that [A070080(n), A070081(n), A070082(n)] is a scalene integer triangle.

8, 13, 17, 20, 21, 25, 29, 30, 33, 36, 37, 41, 42, 44, 45, 49, 50, 53, 56, 57, 59, 60, 62, 66, 67, 69, 70, 74, 75, 77, 78, 79, 80, 83, 86, 87, 89, 90, 92, 96, 97, 99, 100, 101, 102, 105, 106, 110, 111, 113, 114, 115, 116, 119, 122

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..920

Reinhard Zumkeller, Integer-sided triangles

EXAMPLE

a(17)=50: [A070080(50), A070081(50), A070082(50)]=[4<6<8].

MATHEMATICA

m = 55 (* 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] // Flatten (* Jean-François Alcover, Oct 12 2021 *)

CROSSREFS

Cf. A005044, A070113, A070114, A070121, A070122, A070123, A070130, A070131, A070132.

Sequence in context: A129410 A338598 A168339 * A070113 A178968 A006613

Adjacent sequences: A070109 A070110 A070111 * A070113 A070114 A070115

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

STATUS

approved