A119352 Smallest base b > 1 such that n in base b uses no digit b-1.

2, 3, 4, 3, 3, 4, 4, 5, 4, 3, 3, 5, 3, 3, 6, 5, 4, 4, 4, 6, 4, 4, 4, 7, 4, 4, 4, 3, 3, 7, 3, 3, 4, 4, 4, 5, 3, 3, 4, 3, 3, 4, 4, 5, 6, 6, 6, 9, 6, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 7, 5, 5, 5, 5, 4, 4, 4, 5, 4, 4, 4, 7, 4, 4, 4, 5, 5, 5, 5, 6, 4, 3, 3, 5, 3, 3, 4, 5, 4, 4, 3, 3, 5, 3, 3, 9, 4, 4, 4, 6, 4, 4, 4, 7, 4

Offset: 0

Author

Franklin T. Adams-Watters, May 15 2006

Keywords

• base
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A106370, A119353, A119354.

Programs

Haskell

a119352 n = f 2 n where
   f b x = g x where
     g 0 = b
     g z = if r == b - 1 then f (b + 1) n else g z'
           where (z', r) = divMod z b
-- Reinhard Zumkeller, Apr 12 2015

Mathematica

a[n_] := Module[{b = 2}, While[MemberQ[IntegerDigits[n, b], b-1], b++]; b]; Array[a, 100, 0] (* Amiram Eldar, Jul 29 2025 *)

PARI

a(n) = {my(b = 2, d); while(d = digits(n, b); #d > 0 && vecmax(d) == b-1, b++); b;} \\ Amiram Eldar, Jul 29 2025

Formula

7 is 111_2 (has 1), 21_3 (has 2), 13_4 (has 3), but 12_5 (no 4), so a(7) = 5.