A134844 Numbers k such that k contains no zero but k^2 contains at least one zero.

32, 33, 45, 47, 48, 49, 51, 52, 53, 55, 64, 71, 78, 84, 95, 97, 98, 99, 138, 142, 143, 144, 145, 147, 148, 149, 151, 152, 153, 155, 174, 175, 176, 179, 195, 197, 198, 199, 217, 224, 225, 226, 241, 243, 245, 246, 247, 248, 249, 251, 252, 253, 255, 257, 259, 265

Offset: 1

Author

Artur Jasinski, Nov 13 2007

Keywords

• nonn
• base

Comments

Contains all numbers with no zero that start with 32. - Robert Israel, Jun 25 2019

Examples

			a(1)=32 because 1024 = 32^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• J. Browkin, Groebner basis.

Crossrefs

Cf. A052040, A134843, A134845.

Programs

Maple

filter:= proc(n) local L;
  L:= convert(n,base,10);
  if member(0,L) then return false fi;
  L:= convert(n^2,base,10);
  member(0,L)
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 25 2019

Mathematica

a = {}; Do[Do[Do[k = 100s + 10n + m; w = IntegerDigits[k^2]; If[MemberQ[w, 0], AppendTo[a, k]], {n, 1, 9}], {m, 1, 9}], {s, 0, 9}]; Union[a]
Select[Range[300],DigitCount[#,10,0]==0&&DigitCount[#^2,10,0]>0&] (* Harvey P. Dale, Mar 20 2012 *)

Extensions

Definition clarified by Harvey P. Dale, Mar 20 2012