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A321067 Considering Pythagorean triple (a,b,c) with a < b < c, least a such that there exists a primitive triple where c - b is the n-th term of A096033.

%I A321067 #19 Jan 03 2019 09:28:07
%S A321067 3,8,20,33,48,65,88,119,140,204,207,252,297,336,396,429,540,555,616,
%T A321067 696,731,832,893,1036,1113,1140,1248,1311,1428,1525,1692,1748,1809,
%U A321067 1960,2059,2184,2325,2508,2576,2739,2832
%N A321067 Considering Pythagorean triple (a,b,c) with a < b < c, least a such that there exists a primitive triple where c - b is the n-th term of A096033.
%H A321067 Jean-François Alcover, <a href="/A321067/b321067.txt">Table of n, a(n) for n = 1..1000</a>
%e A321067 a(2) = 8 because in the primitive triple (8,15,17), c - b = A096033(2) = 2 and no smaller a yields a primitive triple where a < b < c and c - b = 2.
%t A321067 nmax = 100; kmax = 2;
%t A321067 A096033 = Union[2 Range[nmax]^2, (2 Range[0, Ceiling[nmax/Sqrt[2]]]+1)^2];
%t A321067 r[n_, k_] := Module[{a, b, c}, {a, b, c} /. {ToRules[Reduce[0 < a < b < c && c - b == A096033[[n]] && a^2 + b^2 == c^2, {a, b, c}, Integers] /. C[1] -> k]}];
%t A321067 a[n_] := a[n] = SelectFirst[Flatten[Table[r[n, k], {k, 1, kmax}], 1], GCD @@ # == 1 &] // First;
%t A321067 Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jan 01 2019 *)
%Y A321067 Cf. A096033, A094904.
%K A321067 nonn
%O A321067 1,1
%A A321067 _Jeffrey Burch_, Oct 26 2018