A239590 Numbers whose cubes are cyclops numbers.

0, 42, 115, 116, 123, 135, 163, 164, 199, 498, 525, 557, 562, 564, 576, 579, 596, 615, 623, 642, 661, 666, 695, 697, 717, 721, 724, 748, 788, 806, 827, 886, 945, 961, 994, 2272, 2274, 2319, 2325, 2329, 2391, 2438, 2512, 2529, 2537, 2545, 2617, 2637, 2654

Offset: 1

Author

Colin Barker, Mar 24 2014

Keywords

• nonn
• base

Examples

			123 is in the sequence because 123^3 = 1860867, which is a cyclops number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A000578, A134808, A160711, A239587, A239588, A239589, A239591.

Programs

Mathematica

Join[{0},Select[Range[0,3000],OddQ[IntegerLength[#^3]]&&DigitCount[#^3,10,0]==1&&IntegerDigits[#^3][[(IntegerLength[ #^3]+ 1)/2]] == 0&]] (* Harvey P. Dale, Nov 05 2024 *)

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)}
s=[]; for(n=0, 3000, if(is_cyclops(n^3), s=concat(s, n))); s