A362710 Numbers m such that the decimal expansion of 1/m contains no digit 0, ignoring leading and trailing 0's.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 35, 36, 40, 44, 45, 50, 54, 55, 56, 60, 64, 65, 66, 70, 72, 74, 75, 80, 82, 88, 90, 100, 104, 108, 112, 120, 125, 128, 132, 140, 144, 148, 150, 160, 175, 176, 180, 200, 216, 220, 224, 225, 240, 250, 252, 260, 264

Offset: 1

Author

Robert Israel, Apr 30 2023

Keywords

• nonn
• base

Comments

If k is a term, then so is 10*k.

Examples

			a(12) = 14 is a term because 1/14 = 0.0714285714... contains no digit 0 except for leading 0's.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Complement of A352154. Cf. A362579.

Programs

Maple

removeInitial0:= proc(L) local i;
  for i from 1 to nops(L) do if L[i] <> 0 then return L[i..-1] fi od;
  []
end proc:
filter:= proc(n) local q;
  q:= NumberTheory:-RepeatingDecimal(1/n);
  not(member(0, removeInitial0(NonRepeatingPart(q))) or member(0, RepeatingPart(q)))
end proc:
select(filter, [$1..300]);

Mathematica

Select[Range[500], FreeQ[First[RealDigits[1/#]], 0] &] (* Paolo Xausa, Apr 22 2024 *)

Python

from itertools import count, islice
from sympy import multiplicity, n_order
def A362710_gen(startvalue=1): # generator of terms >= startvalue
    for a in count(max(startvalue,1)):
        m2, m5 = (~a&a-1).bit_length(), multiplicity(5,a)
        k, m = 10**max(m2,m5), 10**(t:=n_order(10,a//(1<A362710_list = list(islice(A362710_gen(),30)) # Chai Wah Wu, May 04 2023