

A216233


Numbers whose squares have 2R1 digits, such that the number represented by leftmost R digits and number represented by rightmost R digits divide each other evenly.


1



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
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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



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



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



