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

1,1

Links

Table of n, a(n) for n=1..27.

Example

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

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 *)

Prog

(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)))}

Crossrefs

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

Sequence in context: A082452 A362792 A049104 * A364718 A102578 A026060

Adjacent sequences: A226785 A226786 A226787 * A226789 A226790 A226791

Keyword

nonn,base

Author

Antonio Roldán, Jun 18 2013

Status

approved