A110939 Triangular Kaprekar-like numbers: numbers k such that the base-10 representation of T(k) = k*(k+1)/2 is the concatenation of two numbers x and y such that x + y = k.

9, 10, 18, 19, 45, 55, 99, 100, 144, 154, 198, 199, 297, 703, 999, 1000, 1296, 1702, 1998, 1999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999, 10000, 12222, 12727, 14949, 15049, 17271, 17344, 17776, 19998, 19999, 22222, 38962, 77778

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

2223 is a member, since the 2223rd triangular number is 2471976 and 247 + 1976 = 2223.

Mathematica

lst = {}; Do[t = n(n + 1)/2; p=10; While[t>p, If[Mod[t, p]+Floor[t/p]==n, AppendTo[lst, n]]; p*=10], {n, 200000}]; lst
Select[Range[10^5], Function[n, Total@ Boole@ Function[k, n == First@ # + Last@ # & /@ Map[FromDigits /@ TakeDrop[IntegerDigits@ k, #] &, Range[IntegerLength@ k - 1]]][n (n + 1)/2] > 0]] (* Michael De Vlieger, May 07 2016, Version 10.2 *)

Crossrefs

Cf. A006886.

Sequence in context: A131417 A268135 A058369 * A260042 A141640 A231504

Adjacent sequences: A110936 A110937 A110938 * A110940 A110941 A110942

Keyword

base,nonn

Author

Giovanni Resta, Jan 21 2006

Status

approved