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A370571
Smallest multiple of n that when written in base 10 uses only 0's and 1's and at least one of each.
1
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
OFFSET
1,1
COMMENTS
For all n, a(n) exists (see proof in References).
REFERENCES
Peter Winkler, Mathematical Puzzles (revised edition), CRC Press, 2024, p. liii.
LINKS
FORMULA
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
MATHEMATICA
a[n_]:=Min[Select[FromDigits/@Tuples[{0, 1}, n+1],
Divisible[#, n]&&Union[IntegerDigits[#]]=={0, 1}&]]; a/@Range[23]
PROG
(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)
print([a(n) for n in range(1, 24)]) # Michael S. Branicky, Feb 22 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ivan N. Ianakiev, Feb 22 2024
EXTENSIONS
More terms from Michael S. Branicky, Feb 22 2024
STATUS
approved