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

Offset: 1

Author

Hans Havermann, Aug 21 2013

Keywords

• nonn
• base

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.

Examples

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

Links

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

Crossrefs

Cf. A045913, A118936, A118938, A228103.

Programs

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}]]

PARI

lista(nn) = my(d, s, t=1, v=List([])); while(t(x>1&&x<=nn), v)); \\ Jinyuan Wang, Jan 02 2025