A202296 The first a(n) positive multiples of n together include every digit.

10, 45, 10, 23, 18, 15, 10, 12, 10, 9, 10, 13, 8, 17, 12, 16, 7, 5, 10, 45, 9, 9, 9, 19, 36, 15, 7, 17, 7, 9, 10, 18, 10, 27, 16, 11, 10, 5, 10, 23, 9, 9, 7, 9, 8, 11, 10, 12, 10, 18, 9, 18, 8, 11, 9, 12, 10, 5, 10, 15, 9, 9, 8, 9, 11, 11, 7, 14, 5, 8, 10, 11

Offset

1,1

Comments

The maximum value of this sequence is a(n) = 72, first attained with n = 125. This can be proved via analysis mod 10^4 (Tomas Rokicki). a(n) = 72 for an infinite number of n including n = 125*10^k.

Links

David W. Wilson, Table of n, a(n) for n = 1..10000

Example

The first 7 multiples of 17 (17,34,51,68,85,102,119) together include every digit, so a(17) = 7.

Mathematica

multInclD[n_, b_:10] := Module[{curr = 1, notFound = True}, While[notFound, If[Union[Flatten[Table[IntegerDigits[n * k, b], {k, curr}]]] == Range[0, b - 1], notFound = False, curr++]]; Return[curr]]; Table[multInclD[n], {n, 70}] (* Alonso del Arte, Dec 15 2011 *)

Prog

(Python)
def a(n):
    s = set()
    return next(i for i in range(1, 73) if len(s:=s|set(str(i*n)))==10)
print([a(n) for n in range(1, 73)]) # Michael S. Branicky, Apr 14 2023

Crossrefs

Sequence in context: A200189 A240383 A160970 * A299530 A238982 A292611

Adjacent sequences: A202293 A202294 A202295 * A202297 A202298 A202299

Keyword

nonn,base

Author

David W. Wilson, Dec 15 2011

Status

approved