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

1,1

Comments

Complement of A003592.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Repeating Decimal

Example

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

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 *)

Prog

(PARI) isok(k) = my(p=5); k>0 && !(#setunion(Set(factor(k)[, 1]), [2, p])==2); \\ Arkadiusz Wesolowski, Mar 08 2026
(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

Crossrefs

Cf. A003592.

Sequence in context: A282140 A071530 A005767 * A176237 A187811 A324696

Adjacent sequences: A085834 A085835 A085836 * A085838 A085839 A085840

Keyword

nonn,easy,nice,base

Author

Eric W. Weisstein, Jul 04 2003

Extensions

Definition corrected by Robert Israel, Jul 09 2014

Status

approved