A286662 - OEIS

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

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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