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A285845 Powers (A001597) that are also cyclops numbers (A134808).

%I A285845 #23 Apr 28 2017 08:34:13
%S A285845 11025,19044,21025,24025,32041,38025,42025,47089,51076,58081,59049,
%T A285845 65025,66049,67081,74088,75076,87025,93025,1110916,1140624,1170724,
%U A285845 1190281,1240996,1270129,1290496,1340964,1350244,1380625,1420864,1430416,1490841,1510441
%N A285845 Powers (A001597) that are also cyclops numbers (A134808).
%C A285845 The first term not in A160711 is 74088 = 42^3.
%C A285845 Intersection of A001597 and A134808. - _Robert G. Wilson v_, Apr 27 2017
%H A285845 Giovanni Resta, <a href="/A285845/b285845.txt">Table of n, a(n) for n = 1..10000</a> (first 1156 terms from Robert G. Wilson v)
%t A285845 Select[NestList[If[# == 1, 4, Min@ Table[(Floor[#^(1/k)] + 1)^k, {k, 2, 1 + Floor@ Log2@ #}]] &, 1, 1400], Function[n, And[OddQ@ Length@ #, #[[ Ceiling[Length[#]/2] ]] == 0, DigitCount[n, 10, 0] == 1] &@ IntegerDigits@ n]] (* _Michael De Vlieger_, Apr 27 2017, after _Robert G. Wilson v_ at A001597 *)
%t A285845 cyclopsQ[n_Integer, b_: 10] := Module[{digitList = IntegerDigits[n, b], len, pos0s, flag}, len = Length[digitList]; pos0s = Select[Range[len], digitList[[#]] == 0 &]; flag = OddQ[len] && (Length[pos0s] == 1) && (pos0s == {(len + 1)/2}); Return[flag]]; (* from Alonso del Arte in A134808 *) min = 0; max = 1520000; t = Union@ Flatten@ Table[n^expo, {expo, Prime@ Range@ PrimePi@ Log2@ max}, {n, Floor[1 + min^(1/expo)], max^(1/expo)}]; Select[t, cyclopsQ] (* _Robert G. Wilson v_, Apr 27 2017 *)
%o A285845 (PARI)
%o A285845 is_cyclops(k) = {
%o A285845   if(k==0, return(1));
%o A285845   my(d=digits(k), j);
%o A285845   if(#d%2==0 || d[#d\2+1]!=0, return(0));
%o A285845   for(j=1, #d\2, if(d[j]==0, return(0)));
%o A285845   for(j=#d\2+2, #d, if(d[j]==0, return(0)));
%o A285845   return(1)}
%o A285845 L=List(); for(n=1, 100000, if(ispower(n) && is_cyclops(n), listput(L, n))); Vec(L)
%Y A285845 Cf. A001597, A134808, A160711.
%K A285845 nonn,base
%O A285845 1,1
%A A285845 _Colin Barker_, Apr 27 2017