A239828
Cyclops numbers which are squares of cyclops numbers.
Original entry on oeis.org
0, 11025, 42025, 93025, 121308196, 121506529, 121903681, 122301481, 144408289, 144504441, 145106116, 145805625, 145902241, 169702729, 169806961, 171505216, 196308121, 196504324, 197205849, 197908624, 198105625, 198302724, 256608361, 256704484, 257409936
Offset: 1
145106116 is in the sequence because 145106116 = 12046^2, and both 145106116 and 12046 are cyclops numbers.
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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)}
s=[]; for(n=0, 100000, if(is_cyclops(n) && is_cyclops(n^2), s=concat(s, n^2))); s
A286662
Numbers k such that k, k^2 and k^3 are cyclops numbers (A134808).
Original entry on oeis.org
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
Offset: 1
16075 is in the sequence because k^2 = 258405625, k^3 = 4153870421875 and these three numbers are cyclops numbers.
Cf.
A000290,
A000578,
A134808,
A160711,
A239587,
A239588,
A239589,
A239590,
A239591,
A239827,
A239828.
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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 *)
-
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)
Showing 1-2 of 2 results.
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