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

0,1

Links

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A106370, A119353, A119354.

Sequence in context: A123699 A322808 A352899 * A205010 A389567 A383362

Adjacent sequences: A119349 A119350 A119351 * A119353 A119354 A119355

Keyword

base,nonn

Author

Franklin T. Adams-Watters, May 15 2006

Status

approved