A085837 Denominators of unit fractions having non-terminating decimal expansions.

3, 6, 7, 9, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84

Offset: 1

Author

Eric W. Weisstein, Jul 04 2003

Keywords

• nonn
• easy
• nice
• base

Comments

Complement of A003592.

Examples

			1/3=0.3333..., 1/6=0.16666..., 1/7=0.142857142857..., ...
		

Links

• Eric Weisstein's World of Mathematics, Repeating Decimal

Crossrefs

Cf. A003592.

Programs

Maple

isA085837 := proc(n)
        return (numtheory[factorset](n) minus {2,5} <> {} );
end proc:
A085837 := proc(n)
    option remember;
    if n = 1 then
        3;
    else
        for a from procname(n-1)+1 do
            if isA085837(a) then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Jul 16 2012

Mathematica

Select[ Range[84], MatchQ[ RealDigits[1/#], {{_, {}}, 0|-1}] &] (* From Jean-François Alcover, Nov 07 2011 *)
Select[Range[100],Depth[RealDigits[1/#]]>3&] (* Harvey P. Dale, May 28 2015 *)

Python

from sympy import integer_log
def A085837(n):
    def f(x): return n+sum((x//5**i).bit_length() for i in range(integer_log(x,5)[0]+1))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Feb 24 2025

Extensions

Definition corrected by Robert Israel, Jul 09 2014