OFFSET
1,2
MATHEMATICA
t = {}; Do[tet = n (n + 1) (n + 2)/6; s = Floor[Sqrt[tet]]; If[s^2 + s == tet, AppendTo[t, tet]], {n, 0, 1000}]; t (* T. D. Noe, Mar 18 2013 *)
With[{nn=50000}, Intersection[Binomial[Range[0, nn]+2, 3], Table[n(n+1), {n, nn}]]] (* Harvey P. Dale, Apr 04 2016 *)
PROG
(Python)
def rootPronic(a):
sr = 1<<33
while a < sr*(sr+1):
sr>>=1
b = sr>>1
while b:
s = sr+b
if a >= s*(s+1):
sr = s
b>>=1
return sr
for i in range(1<<20):
a = i*(i+1)*(i+2)//6
t = rootPronic(a)
if a == t*(t+1):
print(a)
CROSSREFS
KEYWORD
nonn,more,changed
AUTHOR
Alex Ratushnyak, Mar 15 2013
STATUS
approved