A228381 Unabridged sub-Kaprekar numbers (A118936, but allowing powers of ten).

10, 11, 78, 100, 101, 287, 364, 1000, 1001, 1078, 1096, 1287, 1364, 10000, 10001, 11096, 18183, 100000, 100001, 118183, 336634, 1000000, 1000001, 1336634, 2727274, 10000000, 10000001, 12727274, 19138757, 23529412, 25974026, 97744361, 100000000, 100000001, 120879122, 123529412, 140017878, 165991904, 237762239, 288553552, 307692308, 333666334

Offset

1,1

Comments

Square roots of A228103.

Excluding powers-of-ten and powers-of-ten-plus-one, what remains may be arranged into pairs (x,y), y>x, where y-x is a power of ten. The x terms correspond to A118938.

Links

Hans Havermann, Table of n, a(n) for n = 1..1016

Example

10, because 10^2 = (10-0)^2
11, because 11^2 = (12-1)^2
78, because 78^2 = (6-084)^2

Mathematica

k=3; While[k<10^8, k++; s=k^2; d=IntegerDigits[s]; l=Length[d]; Do[a=FromDigits[Take[d, {1, i}]]; b=FromDigits[Take[d, {i+1, l}]]; If[k==Abs[a-b], Print[k]], {i, l-1}]] (* Hans Havermann, Aug 21 2013 *)

Crossrefs

Cf. A045913, A118936, A118938, A228103.

Sequence in context: A122602 A037958 A041214 * A262229 A347182 A331604

Adjacent sequences: A228378 A228379 A228380 * A228382 A228383 A228384

Keyword

nonn,base

Author

Hans Havermann, Aug 21 2013

Status

approved