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 A216267 Numbers that are both tetrahedral and pronic. 0
 0, 20, 56, 7140, 1414910 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Intersection of A000292 and A002378. LINKS 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

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Last modified November 27 07:59 EST 2022. Contains 358362 sequences. (Running on oeis4.)