A239588 Fourth powers that are cyclops numbers.

0, 7890481, 9150625, 623201296, 981506241, 17363069361, 18945044881, 28813025536, 33871089681, 38167092496, 45954068161, 89526025681, 95565066496, 1421970391296, 1551160647936, 1736870953216, 3941340648961, 4771970346256, 5281980641536, 5436960129441

Offset: 1

Author

Colin Barker, Mar 24 2014

Keywords

• nonn
• base

Comments

Intersection of A000583 (Fourth powers) and A134808 (Cyclops numbers).

Links

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

Crossrefs

Cf. A000583, A134808, A160711, A239587, A239589, A239590, A239591.

Programs

Mathematica

cn4Q[n_]:=Module[{idn=IntegerDigits[n],len},len=Length[idn]; OddQ[ len] && idn[[(len+1)/2]]==0&&DigitCount[n,10,0]==1]; Select[Range[0,2000]^4, cn4Q] (* Harvey P. Dale, Dec 20 2015 *)

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, 2000, if(is_cyclops(n^4), s=concat(s, n^4))); s

Formula

a(n) = A239591(n)^4.