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A286662 Numbers k such that k, k^2 and k^3 are cyclops numbers (A134808).

%I A286662 #10 Oct 25 2017 15:58:46
%S A286662 0,16075,18039,1130239,1130363,1130668,1150474,1220156,1230423,
%T A286662 1250928,1290628,1330162,1350478,1390313,1390989,1510414,1510712,
%U A286662 1530314,1530461,1530585,1540896,1540977,1560186,1560324,1570341,1580342,1620244,1620389,1630871,1650288
%N A286662 Numbers k such that k, k^2 and k^3 are cyclops numbers (A134808).
%C A286662 For k = 1130239, k^4 = 1631853457220539336688641 is also a cyclops number.
%e A286662 16075 is in the sequence because k^2 = 258405625, k^3 = 4153870421875 and these three numbers are cyclops numbers.
%t A286662 cycQ[n_]:=DigitCount[n,10,0]==1&&OddQ[IntegerLength[n]]&& IntegerDigits[ n][[(IntegerLength[n]+1)/2]]==0; Join[{0},Table[Select[Range[ 10^n, 10^(n+1)-1],AllTrue[{#,#^2,#^3},cycQ]&],{n,2,6,2}]]//Flatten (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 25 2017 *)
%o A286662 (PARI)
%o A286662 is_cyclops(k) = {
%o A286662   if(k==0, return(1));
%o A286662   my(d=digits(k), j);
%o A286662   if(#d%2==0 || d[#d\2+1]!=0, return(0));
%o A286662   for(j=1, #d\2, if(d[j]==0, return(0)));
%o A286662   for(j=#d\2+2, #d, if(d[j]==0, return(0)));
%o A286662   return(1)}
%o A286662 L=List(); for(n=0, 10000000, if(is_cyclops(n) && is_cyclops(n^2) && is_cyclops(n^3), listput(L, n))); Vec(L)
%Y A286662 Cf. A000290, A000578, A134808, A160711, A239587, A239588, A239589, A239590, A239591, A239827, A239828.
%K A286662 nonn,base
%O A286662 1,2
%A A286662 _Colin Barker_, May 12 2017