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

1,1

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

J. Browkin, Groebner basis.

Example

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

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 *)

Crossrefs

Cf. A052040, A134843, A134845.

Sequence in context: A085259 A054032 A134843 * A151983 A022402 A194768

Adjacent sequences: A134841 A134842 A134843 * A134845 A134846 A134847

Keyword

nonn,base

Author

Artur Jasinski, Nov 13 2007

Extensions

Definition clarified by Harvey P. Dale, Mar 20 2012

Status

approved