

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



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
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OFFSET

1,1


LINKS

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


EXAMPLE

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


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 &]


PROG

(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


CROSSREFS

Cf. A012132.
Sequence in context: A085183 A133759 A188258 * A227149 A042963 A264120
Adjacent sequences: A308392 A308393 A308394 * A308396 A308397 A308398


KEYWORD

nonn


AUTHOR

Ralf Steiner, Jul 31 2019


STATUS

approved



