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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A096033, A094904.

Sequence in context: A272528 A195676 A027299 * A224421 A354317 A143785

Adjacent sequences: A321064 A321065 A321066 * A321068 A321069 A321070

Keyword

nonn

Author

Jeffrey Burch, Oct 26 2018

Status

approved