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Smallest b>1 such that n contains no zeros in its base b representation.
4

%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