A106370 Smallest b>1 such that n contains no zeros in its base b representation.

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, 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, 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

Offset

1,1

Comments

a(n*a(n)+k) <= a(n) for 1<=k<a(n);

a(A106372(n)) = n and a(m) <> n for m < A106372(n);

a(A000225(n)) = 2; a(A032924(n)) = 3 for n <> 5.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

n=20: 20[binary]='101001', 20[ternary]='202',
20[base-4]='110', 20[base-5]='40', all containing at least one zero,
but: 20[base-6]='32', containing no zero therefore a(20)=6.

Prog

(Haskell)
a106370 n = f 2 n where
   f b x = g x where
     g 0 = b
     g z = if r == 0 then f (b + 1) n else g z'
           where (z', r) = divMod z b
-- Reinhard Zumkeller, Apr 12 2015

Crossrefs

Cf. A106371.

Cf. A000225, A032924, A106372, A119352.

Sequence in context: A137467 A261461 A078627 * A128630 A273040 A319982

Adjacent sequences: A106367 A106368 A106369 * A106371 A106372 A106373

Keyword

nonn,base

Author

Reinhard Zumkeller, May 01 2005

Extensions

Typo in comment fixed by Reinhard Zumkeller, Aug 06 2010

Status

approved