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A106371 Representation of n in base b, where b is minimal such that n contains no zeros: b = A106370(n).

%I A106371 #7 Apr 12 2015 18:50:42
%S A106371 1,2,11,11,12,12,111,22,21,22,23,22,111,112,1111,121,122,33,34,32,111,
%T A106371 211,212,44,221,222,123,44,131,132,11111,112,113,114,55,121,211,212,
%U A106371 213,1111,1112,222,1121,1122,231,232,233,143,1211,1212,123,1221,1222,312
%N A106371 Representation of n in base b, where b is minimal such that n contains no zeros: b = A106370(n).
%C A106371 In decimal representation feasible only for bases <= 10; A106371(11) = 360 = 2*11^2 + 10*11^1 + 8*11^0 is the first number which cannot be written zerofree with digits 1..9 in base 11. Therefore this sequence is finite with exactly 359 terms. - _Reinhard Zumkeller_, Apr 12 2015
%H A106371 Reinhard Zumkeller, <a href="/A106371/b106371.txt">Table of n, a(n) for n = 1..359</a>
%o A106371 (Haskell)
%o A106371 a106371 n = a106371_list !! (n-1)
%o A106371 a106371_list = map fromJust $ takeWhile (/= Nothing) $ map f [1..] where
%o A106371    f n = g 2 n where
%o A106371      g b x = h x 0 where
%o A106371        h 0 y = if b <= 10 then Just (a004086 y) else Nothing
%o A106371        h z y = if r == 0 then g (b + 1) n else h z' (10 * y + r)
%o A106371                where (z', r) = divMod z b
%o A106371 -- _Reinhard Zumkeller_, Apr 12 2015
%Y A106371 Cf. A106370, A004086.
%K A106371 nonn,base,fini,full
%O A106371 1,2
%A A106371 _Reinhard Zumkeller_, May 01 2005