A376210 -id:A376210 - cp's OEIS frontend

A376209 Numbers k for which the hypotenuse z=4*k+1 occurs in more than one primitive Pythagorean triangle, such that 2 distinct triangles (x1,y1,z), (x2,y2,z) with opposite parity of their short legs x1 and x2 exist (xi < yi < z).

16, 21, 36, 46, 51, 55, 66, 76, 91, 94, 111, 121, 123, 126, 136, 157, 171, 172, 181, 186, 196, 211, 216, 225, 237, 241, 246, 268, 276, 286, 289, 291, 297, 301, 310, 315, 331, 336, 346, 351, 354, 361, 366, 378, 384, 396, 412, 421, 436, 441, 442, 445, 456, 463, 466

Offset: 1

Hugo Pfoertner, Sep 21 2024

nonn

			See A376210.

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Intersection of A375750 and A376208.

Cf. A376210, A376211.

\\ Uses function is_a376208 from A376208
is(n) = is_a376208(n,0) && is_a376208(n,1)

A376211 Numbers k for which among all possible Pythagorean triangles with the hypotenuse 4*k+1, the minimum of the lengths of the shorter legs is odd.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 22, 24, 28, 36, 37, 39, 45, 46, 48, 55, 58, 66, 67, 69, 78, 79, 84, 88, 91, 94, 97, 105, 108, 115, 120, 130, 135, 136, 139, 142, 153, 154, 163, 168, 171, 172, 177, 190, 192, 193, 199, 205, 210, 213, 220, 231, 232, 234, 237, 238, 252, 253, 267

Offset: 1

Hugo Pfoertner, Sep 21 2024

nonn

			See A376210.

({A087938}-1)/4 is a subsequence.
A094178 \ A376210.
Cf. A375750, A376208.

\\ uses function is_a376210_1 from A376210
is_a376210_1(n,1)

cp's OEIS Frontend

A376209 Numbers k for which the hypotenuse z=4*k+1 occurs in more than one primitive Pythagorean triangle, such that 2 distinct triangles (x1,y1,z), (x2,y2,z) with opposite parity of their short legs x1 and x2 exist (xi < yi < z).

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