A123699 Smallest b such that all digits are distinct in base b representation of n.

1, 2, 3, 4, 3, 3, 3, 4, 4, 5, 3, 4, 4, 4, 3, 5, 5, 4, 3, 5, 3, 5, 5, 4, 6, 6, 4, 4, 5, 4, 6, 6, 4, 6, 4, 4, 7, 5, 4, 5, 6, 5, 7, 4, 4, 7, 5, 5, 4, 4, 5, 4, 5, 4, 5, 4, 4, 5, 5, 6, 8, 6, 6, 9, 5, 5, 7, 6, 5, 5, 5, 7, 5, 7, 4, 5, 5, 4, 5, 5, 6, 5, 6, 5, 5, 5, 7, 7, 5, 6, 6, 8, 7, 6, 5, 5, 5, 8, 4, 11, 5, 5, 5, 7, 5

Offset: 1

Author

Reinhard Zumkeller, Oct 08 2006

Keywords

• nonn
• base

Comments

a(A123700(n)) = n and a(m) <> n for m < A123700(n).

See A126688 for another version of the same sequence. - R. J. Mathar, Jun 15 2008

Examples

			n=10: 1010 [b=2] = 101 [b=3] = 22 [b=4] = 20 [b=5]: a(10)=5;
n=11: 1011 [b=2] = 102 [b=3]: a(11)=3;
n=12: 1100 [b=2] = 110 [b=3] = 30 [b=4]: a(12)=4;
n=13: 1101 [b=2] = 111 [b=3] = 31 [b=4]: a(13)=4;
n=14: 1110 [b=2] = 112 [b=3] = 32 [b=4]: a(14)=4;
n=15: 1111 [b=2] = 120 [b=3]: a(15)=3.
		

Links

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

Crossrefs

Cf. A126688, A123700.

Programs

Mathematica

s={};Do[b=1;Until[id= IntegerDigits[n,b];Length[id]==CountDistinct[id],b++];AppendTo[s,b],{n,2,105}];Join[{1},s] (* James C. McMahon, Nov 24 2024 *)

PARI

a(n) = if (n==1, 1, my(b = 2, do = 1); while (do, vb = digits(n, b); if (#vb == #Set(vb), do = 0, b++); ); b); \\ Michel Marcus, Jun 09 2013; corrected Jun 14 2022

Python

from sympy.ntheory.digits import digits
def distinct(n, b): d = digits(n, b); return len(d) == len(set(d))
def a(n):
    if n == 1: return 1
    b = 2
    while not distinct(n, b): b += 1
    return b
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Jun 15 2022