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A226789 Triangular numbers obtained as the concatenation of n+1 and n. 3
10, 21, 26519722651971, 33388573338856, 69954026995401, 80863378086336 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are only six results less than 10^20

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

26519722651971 is the concatenation of 2651972 and 2651971 and a triangular number, because 26519722651971 = 7282818*7282819/2

MATHEMATICA

TriangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; t = {}; Do[s = FromDigits[Join[IntegerDigits[n+1], 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, 10^7, a=concatint(n+1, n); if(istriang(a), print(a)))}

CROSSREFS

Cf. A003098, A068899, A226742, A226772, A226788.

Sequence in context: A039821 A109326 A080454 * A110367 A104865 A063555

Adjacent sequences:  A226786 A226787 A226788 * A226790 A226791 A226792

KEYWORD

nonn,base

AUTHOR

Antonio Roldán, Jun 18 2013

STATUS

approved

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Last modified January 23 00:58 EST 2018. Contains 298093 sequences.