A094609 Numbers n such that n concatenated with n+1 is triangular.

4, 7, 49, 52, 295, 369, 415, 499, 502, 594, 652, 760, 2254, 4999, 5002, 8827, 10330, 14877, 49999, 50002, 490150, 499999, 500002, 509949, 3347109, 4999999, 5000002, 6983470, 24913494, 49999999, 50000002

Offset

1,1

Comments

Numbers 4, 49, 499, 4999, ...; 52, 502, 5002, 50002, ...; 594, 509949, 500999499, 500099994999, ...; 415, 490150, 499001500, 499900015000, ...; with obvious patterns are members of the sequence. - Vladeta Jovovic, Jun 09 2004

Links

Table of n, a(n) for n=1..31.

Example

E.g. 5253 is triangular so 52 is a member.

Mathematica

triQ[n_] := Block[{k = Floor[ Sqrt[2n]]}, If[ k(k + 1) == 2n, True, False]]; Do[ If[ triQ[ FromDigits[ Join[ IntegerDigits[n], IntegerDigits[n + 1]] ]] == True, Print[ n]], {n, 45000000}] (* Robert G. Wilson v, Jun 09 2004 *)
nctrQ[n_]:=With[{c=FromDigits[Join[IntegerDigits[n], IntegerDigits[n+1]]]}, OddQ[Sqrt[8c+1]]]; Select[Range[50000003], nctrQ] (* Harvey P. Dale, Aug 17 2024 *)

Crossrefs

Cf. A000217.

Sequence in context: A375381 A348625 A192168 * A249936 A049191 A308463

Adjacent sequences: A094606 A094607 A094608 * A094610 A094611 A094612

Keyword

base,nonn

Author

Jason Earls, Jun 06 2004

Extensions

More terms from Robert G. Wilson v, Jun 09 2004

Status

approved