A118936 Sub-Kaprekar numbers: k such that k = |q - r| and k^2 = q*10^m + r, for some m >= 1, q >= 0, 0 <= r < 10^m, with k not a power of 10.

11, 78, 101, 287, 364, 1001, 1078, 1096, 1287, 1364, 10001, 11096, 18183, 100001, 118183, 336634, 1000001, 1336634, 2727274, 10000001, 12727274, 19138757, 23529412, 25974026, 97744361, 100000001, 120879122, 123529412, 140017878

Offset: 1

Author

Giovanni Resta, May 06 2006; corrected May 12 2006

Keywords

• base
• nonn

Comments

Union of A118937 and A118938.

Examples

			287^2 = 82369 and |82 - 369| = 287, so 287 is a term.
1287^2 = 1656369 and |1656 - 369| = 1287, so 1287 is a term.
		

Crossrefs

Cf. A006886, A118937, A118938.

Programs

Mathematica

f[n_] := !IntegerQ@Log[10,n] && Block[{p = 10^Range@Log[10,n^2]}, 0 == Times@@(n-Abs[Floor[n^2/p]-Mod[n^2,p]])]; Select[Range@400000,f]