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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A115528, A116501, A145848.

Sequence in context: A220090 A013684 A233821 * A157246 A186460 A171994

Adjacent sequences: A216230 A216231 A216232 * A216234 A216235 A216236

Keyword

nonn,base

Author

Thomas S. Pedigo, Mar 14 2013

Extensions

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

Comment corrected by Giovanni Resta, Mar 15 2013

Status

approved