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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A143785 A182735

Adjacent sequences:  A321064 A321065 A321066 * A321068 A321069 A321070

KEYWORD

nonn

AUTHOR

Jeffrey Burch, Oct 26 2018

STATUS

approved

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Last modified June 20 04:43 EDT 2021. Contains 345157 sequences. (Running on oeis4.)