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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.
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%I #17 Jul 24 2021 01:13:55

%S 9,10,18,19,45,55,99,100,144,154,198,199,297,703,999,1000,1296,1702,

%T 1998,1999,2223,2728,4879,4950,5050,5292,7272,7777,9999,10000,12222,

%U 12727,14949,15049,17271,17344,17776,19998,19999,22222,38962,77778

%N 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.

%H Paolo P. Lava, <a href="/A110939/b110939.txt">Table of n, a(n) for n = 1..100</a>

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

%t 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

%t 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 *)

%Y Cf. A006886.

%K base,nonn

%O 1,1

%A _Giovanni Resta_, Jan 21 2006