A321784 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)).

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, 31, 41, 27, 25, 29, 15, 17, 25, 19, 23, 31, 21, 17, 19, 9, 11, 19, 17, 29, 37, 23, 27, 33, 19, 31, 47, 37, 49, 65, 43, 39, 45, 23, 29, 43, 33, 41, 55, 37, 31, 35, 17

Offset: 1

Author

Rémy Sigrist, Nov 22 2018

Keywords

• nonn
• tabf

Comments

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

Examples

			The first rows are:
   3
   5, 7, 5
   7, 11, 9, 13, 17, 11, 11, 13, 7
		

Links

• Rémy Sigrist, Rows n = 1..9, flattened
• Index entries related to Pythagorean Triples

Crossrefs

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

Programs

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]];
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]))

Formula

Empirically:

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

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

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