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A227201
Areas of Pythagorean triangles with areas that use all ten decimal digits exactly once.
1
1072493856, 1075948326, 1235976840, 1239084756, 1253684790, 1253894670, 1263984750, 1265738940, 1270953864, 1279635840, 1287349560, 1287463950, 1295738640, 1297836540, 1298647350, 1328405976, 1329754860, 1346589720, 1357962840, 1376925480, 1382974560
OFFSET
1,1
COMMENTS
There are 515 members to the set.
MATHEMATICA
mx = 10^10; mn = mx/10; nn = Ceiling[mx^(1/3)]; If[OddQ[nn], nn + 1]; t = Union[Flatten[Table[If[GCD[u, v] == 1 && Mod[u, 2] + Mod[v, 2] == 1, u v (u^2 - v^2), 0], {u, nn}, {v, u - 1}]]]; t2 = Select[Rest[t], # < mx &]; t3 = {}; Do[num0 = Ceiling[Sqrt[mn/n]]; num1 = Floor[Sqrt[mx/n]]; Do[num = i^2*n; If[Length[Union[IntegerDigits[num]]] == 10, AppendTo[t3, num]], {i, num0, num1}], {n, t2}]; t3 = Union[t3] (* T. D. Noe, Sep 20 2013 *)
CROSSREFS
Cf. A024365.
Sequence in context: A049446 A322684 A322694 * A011580 A017002 A017074
KEYWORD
nonn,base,fini,full
AUTHOR
Charles Kluepfel, Sep 18 2013
STATUS
approved