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
Examples
7 is 111_2 (has 1), 21_3 (has 2), 13_4 (has 3), but 12_5 (no 4), so a(7) = 5.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
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 -
Maple
f:= proc(n) local b; for b from 2 do if not member(b-1,convert(n,base,b)) then return b fi od end proc: map(f, [$0..200]); # Robert Israel, Sep 07 2025 -
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 -
Python
from itertools import count from sympy.ntheory import digits def a(n): return next(b for b in count(2) if b-1 not in digits(n, b)) print([a(n) for n in range(105)]) # Michael S. Branicky, Sep 07 2025