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A239827 Cyclops numbers whose squares are cyclops numbers.

%I A239827 #8 Mar 27 2014 18:40:15
%S A239827 0,105,205,305,11014,11023,11041,11059,12017,12021,12046,12075,12079,
%T A239827 13027,13031,13096,14011,14018,14043,14068,14075,14082,16019,16022,
%U A239827 16044,16072,16075,17012,17091,17094,18014,18039,18075,18086,19016,19029,19037,19058
%N A239827 Cyclops numbers whose squares are cyclops numbers.
%C A239827 Subsequence of A239589.
%H A239827 Giovanni Resta, <a href="/A239827/b239827.txt">Table of n, a(n) for n = 1..10000</a>
%F A239827 a(n) = sqrt(A239828(n)).
%e A239827 12046 is in the sequence because 12046^2 = 145106116, and both 12406 and 145106116 are cyclops numbers.
%o A239827 (PARI)
%o A239827 is_cyclops(k) = {
%o A239827   if(k==0, return(1));
%o A239827   my(d=digits(k), j);
%o A239827   if(#d%2==0 || d[#d\2+1]!=0, return(0));
%o A239827   for(j=1, #d\2, if(d[j]==0, return(0)));
%o A239827   for(j=#d\2+2, #d, if(d[j]==0, return(0)));
%o A239827   return(1)}
%o A239827 s=[]; for(n=0, 100000, if(is_cyclops(n) && is_cyclops(n^2), s=concat(s, n))); s
%Y A239827 Cf. A134808, A239589, A239828.
%K A239827 nonn,base
%O A239827 1,2
%A A239827 _Colin Barker_, Mar 27 2014