A187372 Numbers k such that the decimal digits of 1/k contain every digit at least once.

17, 19, 23, 29, 34, 38, 46, 47, 49, 51, 53, 57, 58, 59, 61, 68, 69, 71, 76, 83, 85, 87, 89, 92, 94, 95, 97, 98, 102, 103, 107, 109, 113, 114, 115, 116, 118, 119, 121, 122, 127, 129, 131, 133, 136, 138, 139, 141, 142, 145, 147, 149, 151, 152, 153, 157, 161, 163, 166, 167, 169, 170, 171, 173, 174, 177, 178, 179, 181, 183, 184, 188

Offset: 1

Author

Michel Lagneau, Mar 09 2011

Keywords

• nonn
• base

Examples

			17 is in the sequence because 1/17 = .0588235294117647 0588235294117647 ...
contains every digit at least once ;
31 is not in the sequence because 1/31 = .032258064516129 032258064516129...
without the digit 7.
		

Crossrefs

Cf. A187614.

Programs

Maple

with(numtheory):Digits:=200:B:={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}: T:=array(1..250)
  : for p from 1 to 200 do:ind:=0:n:=floor(evalf(10^200/p)):l:=length(n):n0:=n:s:=0:for
  m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v : T[m]:=u:od: A:=convert(T,
  set):z:=nops(A):if A intersect B = B and ind=0 then ind:=1: printf(`%d, `, p):else
  fi:od:

Mathematica

A2 := {}; Do[ If[Length[Union[IntegerDigits[Floor[10^200/n]]]] == 10, A2 =
  Join[A2, {n}]], {n, 1, 200}]; Print[A2]