A226788 Triangular numbers obtained as the concatenation of n and n+1.

45, 78, 4950, 5253, 295296, 369370, 415416, 499500, 502503, 594595, 652653, 760761, 22542255, 49995000, 50025003, 88278828, 1033010331, 1487714878, 4999950000, 5000250003, 490150490151, 499999500000, 500002500003, 509949509950, 33471093347110, 49999995000000, 50000025000003

Offset: 1

Author

Antonio Roldán, Jun 18 2013

Keywords

• nonn
• base

Examples

			If n=295, n//n+1 = 295296 = 768*769/2, a triangular number.
		

Crossrefs

Cf. A003098, A068899, A226742, A226772, A226789.

Programs

Mathematica

TriangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; t = {}; Do[s = FromDigits[Join[IntegerDigits[n], IntegerDigits[n+1]]]; If[TriangularQ[s], AppendTo[t, s]], {n, 100000}]; t (* T. D. Noe, Jun 18 2013 *)
Select[FromDigits[Join[Flatten[IntegerDigits[#]]]]&/@Partition[ Range[ 5000010],2,1], OddQ[Sqrt[8#+1]]&] (* Harvey P. Dale, Jun 11 2015 *)

PARI

concatint(a,b)=eval(concat(Str(a),Str(b)))
istriang(x)=issquare(8*x+1)
{for(n=1,10^7,a=concatint(n,n+1);if(istriang(a),print(a)))}