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A055241
Smallest base in which n is not divisible by any of its digits (0 if no such base).
3
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, 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, 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
OFFSET
1,11
LINKS
EXAMPLE
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
MAPLE
f:= proc(n) local b, L;
for b from 3 to n-2 do
L:= convert(convert(n, base, b), set) minus {0};
if andmap(d -> n mod d <> 0, L) then return b fi
od;
0
end proc:
map(f, [$1..100]); # Robert Israel, Oct 29 2024
PROG
(Python)
from sympy.ntheory import digits
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)
print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Oct 29 2024
CROSSREFS
KEYWORD
base,nonn,look,changed
AUTHOR
Henry Bottomley, May 04 2000
STATUS
approved