S001064

Primitive Pythagorean sextuples (a, b, c, d, e, f) sorted.

1, 1, 1, 2, 3, 4, 2, 2, 2, 2, 3, 5, 1, 1, 3, 3, 4, 6, 1, 2, 2, 2, 6, 7, 2, 2, 3, 4, 4, 7, 1, 1, 1, 5, 6, 8, 1, 1, 2, 3, 7, 8, 1, 2, 3, 5, 5, 8, 1, 3, 3, 3, 6, 8, 1, 2, 2, 6, 6, 9, 2, 3, 4, 4, 6, 9, 1, 1, 1, 4, 9, 10, 1, 1, 3, 5, 8, 10, 1, 3, 4, 5, 7, 10

1

Sextuples such that f^2 = e^2 + d^2 + c^2 + b^2 + a^2. There are only a finite number of cases that sum to a given f^2.

T. D. Noe, Plot of 1024 sextuples

T. D. Noe, Table of 1024 sextuples

(Mma) a =.; b =.; c =.; d =.; e =.; t = {}; terms = 0; f = 0; While[terms < 100, f++; sol = Solve[a^2 + b^2 + c^2 + d^2 + e^2 == f^2 && 0 < a <= b <= c <= d <= e <= f, {a, b, c, d, e}, Integers]; If[Length[sol] > 0, t8 = Table[Table[sol[[i]][[j, 2]], {j, 5}], {i, Length[sol]}]; sol = Select[t8, GCD @@ # == 1 &]; If[Length[sol] > 0, sol = Transpose[Join[Transpose[sol], {Table[f, {Length[sol]}]}]]; t = Join[t, Sort[sol]]; terms = terms + Length[sol]]]]; t

Cf.S001069.

nonn,tabl

T. D. Noe, Aug 10 2017