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A286662
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Numbers k such that k, k^2 and k^3 are cyclops numbers (A134808).
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0
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0, 16075, 18039, 1130239, 1130363, 1130668, 1150474, 1220156, 1230423, 1250928, 1290628, 1330162, 1350478, 1390313, 1390989, 1510414, 1510712, 1530314, 1530461, 1530585, 1540896, 1540977, 1560186, 1560324, 1570341, 1580342, 1620244, 1620389, 1630871, 1650288
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OFFSET
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1,2
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COMMENTS
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For k = 1130239, k^4 = 1631853457220539336688641 is also a cyclops number.
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LINKS
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EXAMPLE
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16075 is in the sequence because k^2 = 258405625, k^3 = 4153870421875 and these three numbers are cyclops numbers.
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MATHEMATICA
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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 *)
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PROG
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(PARI)
is_cyclops(k) = {
if(k==0, return(1));
my(d=digits(k), j);
if(#d%2==0 || d[#d\2+1]!=0, return(0));
for(j=1, #d\2, if(d[j]==0, return(0)));
for(j=#d\2+2, #d, if(d[j]==0, return(0)));
return(1)}
L=List(); for(n=0, 10000000, if(is_cyclops(n) && is_cyclops(n^2) && is_cyclops(n^3), listput(L, n))); Vec(L)
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CROSSREFS
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Cf. A000290, A000578, A134808, A160711, A239587, A239588, A239589, A239590, A239591, A239827, A239828.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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