login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
1,1
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: A340289 A133759 A188258 * A227149 A264120 A042963
KEYWORD
nonn
AUTHOR
Ralf Steiner, Jul 31 2019
STATUS
approved