A370571 - OEIS

%I #28 Feb 22 2024 20:19:15

%S 10,10,1011,100,10,1110,1001,1000,1011111111,10,110,11100,1001,10010,

%T 1110,10000,11101,1111111110,11001,100,10101,110,110101,111000,100,

%U 10010,1101111111,100100,1101101,1110,111011,100000,1101111,111010,10010,11111111100,1110,110010,10101,1000

%N Smallest multiple of n that when written in base 10 uses only 0's and 1's and at least one of each.

%C For all n, a(n) exists (see proof in References).

%D Peter Winkler, Mathematical Puzzles (revised edition), CRC Press, 2024, p. liii.

%H Michael S. Branicky, <a href="/A370571/b370571.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%t a[n_]:=Min[Select[FromDigits/@Tuples[{0,1},n+1],

%t Divisible[#,n]&&Union[IntegerDigits[#]]=={0,1}&]]; a/@Range[23]

%o (Python)

%o from itertools import count

%o def a(n): return next(d for k in count(1) if ("0" in (b:=bin(k)[2:])) and (d:=int(b))%n==0)

%o print([a(n) for n in range(1, 24)]) # _Michael S. Branicky_, Feb 22 2024

%Y Cf. A004290, A244859, A007088.

%K nonn,base

%O 1,1

%A _Ivan N. Ianakiev_, Feb 22 2024

%E More terms from _Michael S. Branicky_, Feb 22 2024