A388059 Smallest multiple of n that does not contain the digit 1 in its decimal representation.

2, 2, 3, 4, 5, 6, 7, 8, 9, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 20, 42, 22, 23, 24, 25, 26, 27, 28, 29, 30, 62, 32, 33, 34, 35, 36, 37, 38, 39, 40, 82, 42, 43, 44, 45, 46, 47, 48, 49, 50, 204, 52, 53, 54, 55, 56, 57, 58, 59, 60, 244, 62, 63, 64, 65, 66, 67, 68, 69, 70, 284, 72, 73, 74, 75, 76, 77, 78, 79, 80, 243, 82, 83, 84, 85, 86, 87, 88, 89, 90

Offset

1,1

Links

James C. McMahon, Table of n, a(n) for n = 1..10000

Stackexchange, Multiple of n that does not contain the digit 1 in its decimal representation, (2016).

Example

a(109) = 3*109 because 1*109 = 109 and 2*109 = 218 contain a 1 but 3*109 = 327 does not.

Maple

A388059:= proc(n)
    local k, a;
    for k from 1 do
        a := k*n ;
        if convert(convert(a, base, 10), set) intersect {1} = {} then
            return a;
        end if;
    end do:
end proc:
seq(A388059(n), n=1..150) ;

Mathematica

a[n_]:=Module[{k=1}, While[!ContainsNone[IntegerDigits[k*n], {1}], k++]; k*n]; Array[a, 90] (* James C. McMahon, Sep 14 2025 *)

Prog

(Python)
from itertools import count
def a(n): return next(m for k in count(1) if '1' not in str(m:=n*k))
print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Sep 14 2025

Crossrefs

Cf. A039932, A319542 (indices of records of a(n)/n).

Sequence in context: A118868 A017885 A274165 * A011874 A000115 A367253

Adjacent sequences: A388056 A388057 A388058 * A388060 A388061 A388062

Keyword

nonn,base

Author

R. J. Mathar, Sep 14 2025

Status

approved