This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A216267 #27 Dec 28 2024 10:19:58
%S A216267 0,20,56,7140,1414910
%N A216267 Numbers that are both tetrahedral and pronic.
%C A216267 Intersection of A000292 and A002378.
%C A216267 The equation y*(y+1) = x*(x+1)*(x+2)/6 leads to an elliptic curve, which has a finite number of solutions, all of which are already listed. - _Max Alekseyev_, Dec 28 2024
%t A216267 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 *)
%t A216267 With[{nn=50000},Intersection[Binomial[Range[0,nn]+2,3],Table[n(n+1),{n,nn}]]] (* _Harvey P. Dale_, Apr 04 2016 *)
%o A216267 (Python)
%o A216267 def rootPronic(a):
%o A216267 sr = 1<<33
%o A216267 while a < sr*(sr+1):
%o A216267 sr>>=1
%o A216267 b = sr>>1
%o A216267 while b:
%o A216267 s = sr+b
%o A216267 if a >= s*(s+1):
%o A216267 sr = s
%o A216267 b>>=1
%o A216267 return sr
%o A216267 for i in range(1<<20):
%o A216267 a = i*(i+1)*(i+2)//6
%o A216267 t = rootPronic(a)
%o A216267 if a == t*(t+1):
%o A216267 print(a)
%Y A216267 Cf. A000292, A002378, A027568, A029549, A003556.
%K A216267 nonn,fini,full
%O A216267 1,2
%A A216267 _Alex Ratushnyak_, Mar 15 2013
%E A216267 fini, full keywords added by _Max Alekseyev_, Dec 28 2024