This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
51 is a term because the first three multiples of 51 (51, 102, 153) all contain the digit 1, and 51 is the least positive integer with this property.
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.
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
The first four multiples of 531 are 531, 1062, 1593, and 2124. All of them contain digit 1.
Select[Range[10000], Length[ Position[IntegerDigits[#], 1]] > 0 && Length[ Position[IntegerDigits[2 #], 1]] > 0 && Length[ Position[IntegerDigits[3 #], 1]] > 0 && Length[ Position[IntegerDigits[4 #], 1]] > 0 &]
def ok(n): return all('1' in str(k*n) for k in [1, 2, 3, 4])
print(list(filter(ok, range(5155)))) # Michael S. Branicky, Jun 17 2021
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