A226742 Triangular numbers obtained as the concatenation of 2n and n.

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

Links

Table of n, a(n) for n=1..22.

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

Cf. A003098, A068899, A226772, A226788, A226789.

Sequence in context: A279763 A068986 A219631 * A077400 A041854 A219820

Adjacent sequences: A226739 A226740 A226741 * A226743 A226744 A226745

Keyword

nonn,base

Author

Antonio Roldán, Jun 18 2013

Status

approved