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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

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

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