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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.

%I A216233 #19 Dec 28 2023 19:36:26
%S A216233 245,249,251,255,264,1245,1249,2490,2498,2502,2510,10984,12490,12498,
%T A216233 15449,18735,18751,18868,22714,24980,24996,27907,28302,31225,31249,
%U A216233 31579,101852,124996,139535,152174,187494,187510,218751,238165,249992,279070,281249
%N 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.
%C A216233 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.
%H A216233 Giovanni Resta, <a href="/A216233/b216233.txt">Table of n, a(n) for n = 1..165</a>
%e A216233 The square of 22714 is 515925796, and 51592 = 2*25796.
%t A216233 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 *)
%Y A216233 Cf. A115528, A116501, A145848.
%K A216233 nonn,base
%O A216233 1,1
%A A216233 _Thomas S. Pedigo_, Mar 14 2013
%E A216233 Missing a(25) and a(27)-a(37) from _Giovanni Resta_, Mar 15 2013
%E A216233 Comment corrected by _Giovanni Resta_, Mar 15 2013