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A055241 Smallest base in which n is not divisible by any of its digits (0 if no such base).

%I A055241 #12 Oct 29 2024 08:26:34
%S A055241 0,0,0,0,0,0,0,0,0,0,4,0,5,0,0,0,5,0,5,0,8,6,5,0,7,7,10,0,6,0,7,9,7,6,
%T A055241 4,0,7,7,7,11,7,0,4,12,16,7,4,0,9,11,9,9,5,10,8,10,10,9,4,0,8,8,11,11,
%U A055241 5,14,5,9,9,11,9,13,5,10,11,10,5,10,5,11,11,11,10,15,5,10,10,13,5,19
%N A055241 Smallest base in which n is not divisible by any of its digits (0 if no such base).
%H A055241 Robert Israel, <a href="/A055241/b055241.txt">Table of n, a(n) for n = 1..10000</a>
%e A055241 a(11)=4 because it is written as 111111111111 in base 1, 1011 in base 2, 102 in base 3 and 23 in base 4; 11 is divisible by 1 but not by 2 or 3
%p A055241 f:= proc(n) local b,L;
%p A055241   for b from 3 to n-2 do
%p A055241     L:= convert(convert(n,base,b),set) minus {0};
%p A055241     if andmap(d -> n mod d <> 0, L) then return b fi
%p A055241   od;
%p A055241   0
%p A055241 end proc:
%p A055241 map(f, [$1..100]); # _Robert Israel_, Oct 29 2024
%o A055241 (Python)
%o A055241 from sympy.ntheory import digits
%o A055241 def a(n): return next((b for b in range(3, n-2) if not any(n%d==0 for d in digits(n, b)[1:] if d > 0)), 0)
%o A055241 print([a(n) for n in range(1, 91)]) # _Michael S. Branicky_, Oct 29 2024
%Y A055241 Cf. A055238-A055242.
%K A055241 base,nonn,look
%O A055241 1,11
%A A055241 _Henry Bottomley_, May 04 2000