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A370571
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Smallest multiple of n that when written in base 10 uses only 0's and 1's and at least one of each.
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1
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10, 10, 1011, 100, 10, 1110, 1001, 1000, 1011111111, 10, 110, 11100, 1001, 10010, 1110, 10000, 11101, 1111111110, 11001, 100, 10101, 110, 110101, 111000, 100, 10010, 1101111111, 100100, 1101101, 1110, 111011, 100000, 1101111, 111010, 10010, 11111111100, 1110, 110010, 10101, 1000
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OFFSET
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1,1
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COMMENTS
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For all n, a(n) exists (see proof in References).
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REFERENCES
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Peter Winkler, Mathematical Puzzles (revised edition), CRC Press, 2024, p. liii.
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LINKS
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FORMULA
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a(10^e-1) <= 1^e 0 1^(8*e), where ^ denotes repeated concatenation of digits on the right-hand side. - Michael S. Branicky, Feb 22 2024
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MATHEMATICA
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a[n_]:=Min[Select[FromDigits/@Tuples[{0, 1}, n+1],
Divisible[#, n]&&Union[IntegerDigits[#]]=={0, 1}&]]; a/@Range[23]
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PROG
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(Python)
from itertools import count
def a(n): return next(d for k in count(1) if ("0" in (b:=bin(k)[2:])) and (d:=int(b))%n==0)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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