

A321769


Consider the tree of triples P(n, k) with n > 0 and 0 < k <= 3^(n1), such that P(1, 1) = [3; 4; 5] and each triple t on some row branches to the triples A*t, B*t, C*t on the next row (with A = [1, 2, 2; 2, 1, 2; 2, 2, 3], B = [1, 2, 2; 2, 1, 2; 2, 2, 3] and C = [1, 2, 2; 2, 1, 2; 2, 2, 3]); T(n, k) is the second component of P(n, k).


7



4, 12, 20, 8, 24, 48, 28, 80, 120, 36, 56, 72, 12, 40, 88, 60, 208, 304, 84, 168, 224, 44, 176, 336, 180, 456, 696, 220, 288, 360, 52, 140, 252, 120, 252, 396, 136, 132, 156, 16, 60, 140, 104, 396, 572, 152, 340, 460, 96, 468, 884, 464, 1140, 1748, 560, 700
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OFFSET

1,1


COMMENTS

The tree P runs uniquely through every primitive Pythagorean triple.
See A321768 for additional comments about P.
All terms are even.


LINKS

Rémy Sigrist, Rows n = 1..9, flattened
Wikipedia, Tree of primitive Pythagorean triples
Index entries related to Pythagorean Triples


FORMULA

Empirically:
 T(n, 1) = A046092(n),
 T(n, (3^(n1) + 1)/2) = A046729(n),
 T(n, 3^(n1)) = 4 * n.


EXAMPLE

The first rows are:
4
12, 20, 8
24, 48, 28, 80, 120, 36, 56, 72, 12


PROG

(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^(n1)+k1, 3)); for (i=2, #d, t = M[d[i]+1] * t); return (t[2, 1])


CROSSREFS

See A321768 and A321770 for the other components.
Cf. A046092, A046729.
Sequence in context: A240762 A050021 A239662 * A133096 A309085 A104814
Adjacent sequences: A321766 A321767 A321768 * A321770 A321771 A321772


KEYWORD

nonn,tabf


AUTHOR

Rémy Sigrist, Nov 18 2018


STATUS

approved



