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

1,1

Comments

Union of A118937 and A118938.

Links

Table of n, a(n) for n=1..29.

Example

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

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]

Crossrefs

Cf. A006886, A118937, A118938.

Sequence in context: A322877 A226708 A206529 * A041224 A030054 A225896

Adjacent sequences: A118933 A118934 A118935 * A118937 A118938 A118939

Keyword

base,nonn

Author

Giovanni Resta, May 06 2006; corrected May 12 2006

Status

approved