A239590 - OEIS

%I #14 Nov 05 2024 16:45:24

%S 0,42,115,116,123,135,163,164,199,498,525,557,562,564,576,579,596,615,

%T 623,642,661,666,695,697,717,721,724,748,788,806,827,886,945,961,994,

%U 2272,2274,2319,2325,2329,2391,2438,2512,2529,2537,2545,2617,2637,2654

%N Numbers whose cubes are cyclops numbers.

%H Colin Barker, <a href="/A239590/b239590.txt">Table of n, a(n) for n = 1..1500</a>

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

%t 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 *)

%o (PARI)

%o is_cyclops(k) = {

%o   if(k==0, return(1));

%o   my(d=digits(k), j);

%o   if(#d%2==0 || d[#d\2+1]!=0, return(0));

%o   for(j=1, #d\2, if(d[j]==0, return(0)));

%o   for(j=#d\2+2, #d, if(d[j]==0, return(0)));

%o   return(1)}

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

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

%K nonn,base

%O 1,2

%A _Colin Barker_, Mar 24 2014