%I #8 Apr 12 2015 18:50:13
%S 2,3,2,3,3,4,2,3,4,4,4,5,3,3,2,3,3,5,5,6,4,3,3,5,3,3,4,6,4,4,2,5,5,5,
%T 6,5,4,4,4,3,3,4,3,3,4,4,4,5,3,3,6,3,3,4,4,5,4,4,4,7,4,4,2,5,6,5,3,3,
%U 5,3,3,5,5,5,7,3,3,7,3,3,5,5,5,5,4,4,4,5,4,4,4,5,4,4,4,5,5,5,5,6,4,4,4,6,4
%N Smallest b>1 such that n contains no zeros in its base b representation.
%C a(n*a(n)+k) <= a(n) for 1<=k<a(n);
%C a(A106372(n)) = n and a(m) <> n for m < A106372(n);
%C a(A000225(n)) = 2; a(A032924(n)) = 3 for n <> 5.
%H Reinhard Zumkeller, <a href="/A106370/b106370.txt">Table of n, a(n) for n = 1..10000</a>
%e n=20: 20[binary]='101001', 20[ternary]='202',
%e 20[base-4]='110', 20[base-5]='40', all containing at least one zero,
%e but: 20[base-6]='32', containing no zero therefore a(20)=6.
%o (Haskell)
%o a106370 n = f 2 n where
%o f b x = g x where
%o g 0 = b
%o g z = if r == 0 then f (b + 1) n else g z'
%o where (z', r) = divMod z b
%o -- _Reinhard Zumkeller_, Apr 12 2015
%Y Cf. A106371.
%Y Cf. A000225, A032924, A106372, A119352.
%K nonn,base
%O 1,1
%A _Reinhard Zumkeller_, May 01 2005
%E Typo in comment fixed by _Reinhard Zumkeller_, Aug 06 2010