A308395 Numbers y such that x*(x+1) + y*(y+1) = z*(z+1) is solvable in positive integers x, z with x <= y.

2, 5, 6, 9, 10, 13, 14, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 37, 38, 39, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 61, 62, 65, 66, 68, 69, 70, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 97

Offset: 1

Author

Ralf Steiner, Jul 31 2019

Keywords

• nonn

Examples

			14 is a term because 14*15 + 14*15 = 20*21.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A012132.

Programs

Mathematica

max = 220; lst = {}; For[x = 1, x < max, x++,
For[y = x, y < max, y++,
  For[z = y, z < max, z++,
   If[x (x + 1) + y (y + 1) == z (z + 1),
    lst = AppendTo[lst, y]]]]]; Select[Union[lst], # < max/2 &]

Python

from sympy import integer_nthroot
A308395_list, y, w = [], 1, 0
while len(A308395_list) < 10000:
    w += y
    z = 0
    for x in range(1,y+1):
        z += x
        if integer_nthroot(8*(w+z)+1,2)[1]:
            A308395_list.append(y)
            break
    y += 1 # Chai Wah Wu, Aug 02 2019