login
A226742
Triangular numbers obtained as the concatenation of 2n and n.
3
21, 105, 2211, 9045, 222111, 306153, 742371, 890445, 1050525, 22221111, 88904445, 107905395, 173808690, 2222211111, 8889044445, 12141260706, 15754278771, 222222111111, 888890444445, 22222221111111, 36734701836735, 65306123265306
OFFSET
1,1
EXAMPLE
If n=111, 2n=222, 2n//n = 222111 = 666*667/2, a triangular number.
MATHEMATICA
TriangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; t = {}; Do[s = FromDigits[Join[IntegerDigits[2*n], IntegerDigits[n]]]; If[TriangularQ[s], AppendTo[t, s]], {n, 100000}]; t (* T. D. Noe, Jun 18 2013 *)
PROG
(PARI)
concatint(a, b)=eval(concat(Str(a), Str(b)))
istriang(x)=issquare(8*x+1)
{for(n=1, 10^5, a=concatint(2*n, n); if(istriang(a), print(a)))}
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antonio Roldán, Jun 18 2013
STATUS
approved