A216267 Numbers that are both tetrahedral and pronic.

0, 20, 56, 7140, 1414910

Offset

1,2

Comments

Intersection of A000292 and A002378.

Links

Table of n, a(n) for n=1..5.

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 = 1L<<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

Cf. A000292, A002378, A027568, A029549, A003556.

Sequence in context: A344072 A109806 A331774 * A012483 A051872 A297397

Adjacent sequences: A216264 A216265 A216266 * A216268 A216269 A216270

Keyword

nonn,more

Author

Alex Ratushnyak, Mar 15 2013

Status

approved