A296606 -id:A296606 - cp's OEIS frontend

A298849 Numbers n where d*n contains the digit d for all of d = 1,2,3,4,5,6,7,8,9.

1, 10, 11, 21, 31, 41, 51, 61, 71, 81, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 121, 131, 141, 151, 161, 171, 181, 191, 201, 210, 211, 221, 231, 241, 251, 261, 271, 281, 291, 301, 310, 311, 321, 331, 341, 351, 361, 371, 381, 391, 401, 410, 411, 421

Offset: 1

J. Lowell, Jan 27 2018

Includes all numbers whose rightmost nonzero digit is a 1.

			12 times 5 = 60, which doesn't contain the digit 5; so 12 is not in this sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A296606.

filter:= n -> andmap(d -> has(convert(d*n,base,10),d), [$1..9]):
select(filter, [$1..1000]); # Robert Israel, Feb 27 2018

Select[Range[421], Function[n, NoneTrue[Range@ 9, FreeQ[IntegerDigits[n #], #] &]]] (* Michael De Vlieger, Jan 28 2018 *)

isok(n) = {for (d=1, 9, if (! vecsearch(Set(digits(d*n)), d), return (0));); return(1);} \\ Michel Marcus, Jan 27 2018

More terms from Michel Marcus, Jan 27 2018

A337084 a(n) is the smallest nonzero digit d whose product d*n will contain the digit d, or 0 if no such digit exists.

Original entry on oeis.org

1, 0, 5, 0, 5, 2, 5, 0, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 9, 5, 0, 5, 2, 5, 6, 5, 5, 1, 0, 5, 0, 4, 2, 4, 0, 5, 0, 1, 0, 5, 3, 3, 2, 5, 8, 5, 5, 1, 0, 5, 7, 5, 2, 5, 0, 5, 2, 1, 2, 2, 2, 5, 2, 5, 7, 5, 5, 1, 0, 5, 0, 5, 2, 3, 3, 3, 0, 1, 7

Offset: 1

J. Lowell, Aug 14 2020

a(n) = 1 for all numbers that contain the digit 1.
For all numbers with 6 followed by a digit in the 0-4 interval, a(n) is 1 or 2.
For all numbers with an odd digit followed by a 0, a(n) is in the 1-5 interval.

			a(22) = 9 because none of 22*1 to 22*8 contain the digit that we multiplied 22 by to get the product, but 22*9 = 198 which contains the digit 9.

Indices of 0's give A296606.

Indices of 1's give A011531.

a[n_] := Module[{d = 1}, While[d < 10 && ! MemberQ[IntegerDigits[n*d], d], d++]; If[d < 10, d, 0]]; Array[a, 100] (* Amiram Eldar, Aug 15 2020 *)

a(n) = {for (d=1, 9, if (#select(x->(x==d), digits(n*d)), return (d));); return (0);} \\ Michel Marcus, Sep 13 2020

cp's OEIS Frontend

A298849 Numbers n where d*n contains the digit d for all of d = 1,2,3,4,5,6,7,8,9.

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