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A068968 Sides of integer Heronian triangles [A068967(n), prime(A068967(n)), a(n)] with area A068969(n). 3
4, 35, 120, 113, 130, 260, 319, 252, 372, 609, 595, 1905, 2020, 5712, 5790, 6148, 7735, 8789, 13651, 14126, 14576, 14725, 19856, 25907, 29603, 36366, 41425, 44325, 53628, 66164, 67830, 103525, 141044, 164396, 229121, 223805, 367336, 366860, 446405, 447855, 538135 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..120

Eric Weisstein's World of Mathematics, Heronian Triangle.

EXAMPLE

a(5) = 37: [37, A000040(37), A068968(5)] = [37,157,130], with s = (36+157+130)/2 = 162: Area^2 = s*(s-37)*(s-157)*(s-130) = 162*125*5*32 = 3240000 = 1800*1800, therefore A068969(5) = 1800.

MATHEMATICA

area[{a_, b_, c_}] := Block[{s = (a + b + c)/2}, Sqrt[s (s-a) (s-b) (s-c)]]; zz[n_] := Block[{s, p = Prime[n], t, z, A}, s = Solve[(n^2 - 2 n p + p^2 - z) (z - n^2 - 2 n p - p^2) == t^2 && z>0 && t>0, {t, z}, Integers]; If[s == {}, {}, z = Sort@ Select[Sqrt[z /. s], IntegerQ]]; Select[Table[{n, p, e}, {e, z}], IntegerQ[A = area[#]] && A > 0 &]]; (Join @@ Parallelize@ Array[zz, 4300])[[All, 3]] (* Giovanni Resta, Apr 20 2020 *)

CROSSREFS

Sequence in context: A297546 A257600 A211612 * A228887 A185592 A296280

Adjacent sequences:  A068965 A068966 A068967 * A068969 A068970 A068971

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 30 2002

EXTENSIONS

Erroneous term 21254 removed and more terms from Giovanni Resta, Apr 20 2020

STATUS

approved

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Last modified December 9 06:07 EST 2021. Contains 349627 sequences. (Running on oeis4.)