A321784 - OEIS

%I #24 Dec 01 2018 05:01:25

%S 3,5,7,5,7,11,9,13,17,11,11,13,7,9,15,13,21,27,17,19,23,13,19,29,23,

%T 31,41,27,25,29,15,17,25,19,23,31,21,17,19,9,11,19,17,29,37,23,27,33,

%U 19,31,47,37,49,65,43,39,45,23,29,43,33,41,55,37,31,35,17

%N Triangle T(n, k) read by rows, n > 0 and 0 < k <= 3^(n-1): T(n, k) = sqrt(A321769(n, k) + A321770(n, k)).

%C This sequence and A321785 are related to a parametrization of the primitive Pythagorean triples in the tree described in A321768.

%H Rémy Sigrist, <a href="/A321784/b321784.txt">Rows n = 1..9, flattened</a>

%H <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a>

%F Empirically:

%F - T(n, 1) = 2*n + 1,

%F - T(n, (3^(n-1) + 1)/2) = A001333(n+1),

%F - T(n, 3^(n-1)) = 2*n + 1.

%e The first rows are:

%e    3

%e    5, 7, 5

%e    7, 11, 9, 13, 17, 11, 11, 13, 7

%o (PARI) M = [[1, -2, 2; 2, -1, 2; 2, -2, 3], [1, 2, 2; 2, 1, 2; 2, 2, 3], [-1, 2, 2; -2, 1, 2; -2, 2, 3]];

%o T(n, k) = my (t=[3; 4; 5], d=digits(3^(n-1)+k-1, 3)); for (i=2, #d, t = M[d[i]+1] * t); return (sqrtint(t[2, 1] + t[3, 1]))

%Y Cf. A001333, A321768, A321769, A321770, A321785.

%K nonn,tabf

%O 1,1

%A _Rémy Sigrist_, Nov 22 2018