A317180 a(n) is the least positive multiple of n that contains at least one digit 1 in its decimal representation.

1, 10, 12, 12, 10, 12, 14, 16, 18, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100, 21, 110, 115, 120, 100, 104, 81, 112, 116, 120, 31, 128, 132, 102, 105, 108, 111, 114, 117, 120, 41, 126, 129, 132, 135, 138, 141, 144, 147, 100, 51, 104, 106, 108, 110, 112, 114

Offset: 1

Author

Rémy Sigrist, Jul 23 2018

Keywords

• nonn
• base

Examples

			The multiples of 3 are: 3, 6, 9, 12, 15, etc.; 12 is the first one containing the digit 1, hence a(3) = 12.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A011531, A187285, A317173.

Programs

Mathematica

on1[n_]:=Module[{k=1},While[DigitCount[k*n,10,1]<1,k++];k*n]; Array[on1,60] (* Harvey P. Dale, Apr 09 2022 *)

PARI

a(n) = forstep (m=n, oo, n, if (setsearch(Set(digits(m)), 1), return (m)))

Formula

a(n) = n * A317173(n).

a(n) <= A187285(n).

Extensions

Definition clarified by Harvey P. Dale, Apr 09 2022