A362579 Numbers k such that the decimal expansion of 1/k does not contain the digit 5.

1, 3, 5, 6, 9, 10, 11, 12, 13, 15, 21, 24, 25, 27, 30, 33, 36, 37, 41, 44, 45, 48, 50, 52, 55, 60, 72, 73, 75, 77, 84, 88, 90, 91, 96, 99, 100, 101, 110, 111, 120, 123, 125, 130, 135, 137, 143, 144, 150, 159, 165, 205, 208, 210, 216, 225, 231, 237, 239, 240, 250, 259, 264, 270, 271, 273, 275, 288

Offset: 1

Author

Robert Israel, Apr 25 2023

Keywords

• nonn
• base

Comments

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

Examples

			a(8) = 12 is a term because 1/12 = 0.08333... does not contain the digit 5.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..2692 (n = 1..1000 from Robert Israel)

Crossrefs

Complement of A353441.

Programs

Maple

filter:= proc(n) local q;
  q:= NumberTheory:-RepeatingDecimal(1/n);
  not(member(5,RepeatingPart(q)) or member(5, NonRepeatingPart(q)))
end proc:
select(filter, [$1..300]);

Mathematica

Select[Range[500], FreeQ[First[RealDigits[1/#]], 5] &] (* Paolo Xausa, Apr 23 2024 *)

Python

from itertools import count, islice
from sympy import multiplicity, n_order
def A362579_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**n_order(10,a//(1<A362579_list = list(islice(A362579_gen(),20)) # Chai Wah Wu, May 01 2023