A239827 Cyclops numbers whose squares are cyclops numbers.

0, 105, 205, 305, 11014, 11023, 11041, 11059, 12017, 12021, 12046, 12075, 12079, 13027, 13031, 13096, 14011, 14018, 14043, 14068, 14075, 14082, 16019, 16022, 16044, 16072, 16075, 17012, 17091, 17094, 18014, 18039, 18075, 18086, 19016, 19029, 19037, 19058

Offset: 1

Author

Colin Barker, Mar 27 2014

Keywords

• nonn
• base

Comments

Subsequence of A239589.

Examples

			12046 is in the sequence because 12046^2 = 145106116, and both 12406 and 145106116 are cyclops numbers.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A134808, A239589, A239828.

Programs

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, 100000, if(is_cyclops(n) && is_cyclops(n^2), s=concat(s, n))); s

Formula

a(n) = sqrt(A239828(n)).