A126688 Lowest base in which n has distinct digits.

2, 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

Offset: 1

Author

Paul Richards, Feb 15 2007

Keywords

• nonn
• base

Comments

Start with binary and work upwards, expressing n in the given base (2,3,4... b). The term a(n)=b is the lowest base in which no two digits in n are the same.

See A123699 for another version of the same sequence. - R. J. Mathar, Jun 15 2008

Examples

			75 is 1001011 in binary (base 2), 2210 in base 3 and 1023 in base 4. So a(75) = 4 since 1023 has distinct digits (and neither 1001011 nor 2210 do).
		

Crossrefs

Cf. A010784 (base 10), A062813 (gives lower bound for a term).

Programs

Mathematica

Table[ b=1;Until[Length[Union[IntegerDigits[n,b]]]==Length[IntegerDigits[n,b]],b++];b,{n,100}] (* James C. McMahon, Dec 26 2024 *)