A216233 Numbers whose squares have 2R-1 digits, such that the number represented by leftmost R digits and number represented by rightmost R digits divide each other evenly.

245, 249, 251, 255, 264, 1245, 1249, 2490, 2498, 2502, 2510, 10984, 12490, 12498, 15449, 18735, 18751, 18868, 22714, 24980, 24996, 27907, 28302, 31225, 31249, 31579, 101852, 124996, 139535, 152174, 187494, 187510, 218751, 238165, 249992, 279070, 281249

Offset: 1

Author

Thomas S. Pedigo, Mar 14 2013

Keywords

• nonn
• base

Comments

Trivial solutions where the rightmost R digits are all zeros have been omitted. The first indices k for which the rightmost R digits of a(k)^2 do not contain leading zeros are 5, 12, 15, 19, 26, 27, 30, 34, 39, 52, 53, 62, 67, 80.

Examples

			The square of 22714 is 515925796, and 51592 = 2*25796.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..165

Crossrefs

Cf. A115528, A116501, A145848.

Programs

Mathematica

cnt = 0; Do[p = 10^Floor[nd/2]; Do[x = Floor[n*n/p]; y = Mod[n*n, 10*p]; If[y>0 && Mod[x,y]*Mod[y,x] == 0, Print[++cnt, " ", n, " ", n*n]], {n, p, Floor[10^(nd/2)]}], {nd,3,11,2}] (* Giovanni Resta, Mar 15 2013 *)

Extensions

Missing a(25) and a(27)-a(37) from Giovanni Resta, Mar 15 2013

Comment corrected by Giovanni Resta, Mar 15 2013