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A238376
Smallest other side of an Heronian triangle with a side of length n.
1
4, 3, 3, 5, 15, 5, 10, 6, 13, 5, 4, 13, 4, 10, 8, 15, 20, 7, 10, 26, 123, 7, 3, 3, 29, 15, 5, 5, 68, 20, 25, 15, 8, 15, 12, 25, 10, 9, 9, 20, 61, 15, 12, 75, 250, 14, 105, 6, 4, 5, 4, 45, 12, 25, 60, 10, 68, 10, 11, 39, 16, 40, 7, 35, 85, 7, 29, 9, 447, 21, 9
OFFSET
3,1
LINKS
EXAMPLE
a(8) = 5 because (8,5,5) is Heronian triangle, and there are no such triangles with one side equal to 8 and another equal to 1, 2, 3 or 4.
MATHEMATICA
area[a_, b_, c_] := Block[{p=(a+b+c)/2}, Sqrt[p*(p-a)*(p-b)*(p-c)]]; a[n_] := Catch@ Block[{b = 0, c}, While[True, b++; Do[If[ IntegerQ[area[n, b, c]], Throw@b], {c, Max[Abs[n-b] + 1, b], n+b-1}]]] /; n > 2; a/@ Range[3, 50]
CROSSREFS
Cf. A055527.
Sequence in context: A372049 A154913 A154915 * A237197 A006994 A038627
KEYWORD
nonn
AUTHOR
Giovanni Resta, Feb 25 2014
STATUS
approved