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.

3, 8, 20, 33, 48, 65, 88, 119, 140, 204, 207, 252, 297, 336, 396, 429, 540, 555, 616, 696, 731, 832, 893, 1036, 1113, 1140, 1248, 1311, 1428, 1525, 1692, 1748, 1809, 1960, 2059, 2184, 2325, 2508, 2576, 2739, 2832

Offset: 1

Author

Jeffrey Burch, Oct 26 2018

Keywords

• nonn

Examples

			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.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A096033, A094904.

Programs

Mathematica

nmax = 100; kmax = 2;
A096033 = Union[2 Range[nmax]^2, (2 Range[0, Ceiling[nmax/Sqrt[2]]]+1)^2];
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]}];
a[n_] := a[n] = SelectFirst[Flatten[Table[r[n, k], {k, 1, kmax}], 1], GCD @@ # == 1 &] // First;
Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 01 2019 *)