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

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

1,2

Comments

For k = 1130239, k^4 = 1631853457220539336688641 is also a cyclops number.

Links

Table of n, a(n) for n=1..30.

Example

16075 is in the sequence because k^2 = 258405625, k^3 = 4153870421875 and these three numbers are cyclops numbers.

Mathematica

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 *)

Prog

(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)

Crossrefs

Cf. A000290, A000578, A134808, A160711, A239587, A239588, A239589, A239590, A239591, A239827, A239828.

Sequence in context: A031839 A062674 A274680 * A222419 A252603 A335305

Adjacent sequences: A286659 A286660 A286661 * A286663 A286664 A286665

Keyword

nonn,base

Author

Colin Barker, May 12 2017

Status

approved