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

1, 2, 11, 11, 12, 12, 111, 22, 21, 22, 23, 22, 111, 112, 1111, 121, 122, 33, 34, 32, 111, 211, 212, 44, 221, 222, 123, 44, 131, 132, 11111, 112, 113, 114, 55, 121, 211, 212, 213, 1111, 1112, 222, 1121, 1122, 231, 232, 233, 143, 1211, 1212, 123, 1221, 1222, 312

Offset: 1

Author

Reinhard Zumkeller, May 01 2005

Keywords

• nonn
• base
• fini
• full

Comments

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..359

Crossrefs

Cf. A106370, A004086.

Programs

Haskell

a106371 n = a106371_list !! (n-1)
a106371_list = map fromJust $ takeWhile (/= Nothing) $ map f [1..] where
   f n = g 2 n where
     g b x = h x 0 where
       h 0 y = if b <= 10 then Just (a004086 y) else Nothing
       h z y = if r == 0 then g (b + 1) n else h z' (10 * y + r)
               where (z', r) = divMod z b
-- Reinhard Zumkeller, Apr 12 2015