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A202296 The first a(n) positive multiples of n together include every digit. 1
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 (list; graph; refs; listen; history; text; internal format)
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 (T. Rockicki). 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 *)

CROSSREFS

Sequence in context: A200189 A240383 A160970 * A238982 A275623 A245871

Adjacent sequences:  A202293 A202294 A202295 * A202297 A202298 A202299

KEYWORD

nonn,base

AUTHOR

David W. Wilson, Dec 15 2011

STATUS

approved

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Last modified August 23 13:52 EDT 2017. Contains 291004 sequences.