A123699 -id:A123699 - cp's OEIS frontend

A123700 Smallest m such that A123699(m) = n.

1, 2, 3, 4, 10, 25, 37, 61, 64, 173, 100, 1020, 1565, 1595, 2323, 3013, 3771, 11838, 9266, 30407, 56267, 46865, 117612, 143083, 216156, 412555, 413711, 818330, 1846411, 2432526, 2094521, 6909827, 15457515, 12960133, 40274514, 30277528, 53521510, 171018877, 81281761

Offset: 1

Reinhard Zumkeller, Oct 09 2006

In base n representation of a(n) all digits are distinct; this is not the case in all base b representations where b is smaller than n. And for numbers m that are smaller than a(n) exists at least one b such that in base b representation of m all digits are distinct.

			a(16)=3013 = 101111000101 [b=2] = 11010121 [b=3] = 233011 [b=4] = 44023 [b=5] = 21541 [b=6] = 11533 [b=7] = 5705 [b=8] = 4117 [b=9] = 3013 [b=10] = 229A [b=11] = 18B1 [b=12] = 14AA [b=13] = 1153 [b=14] = D5D [b=15] = BC5 [b=16] distinct digits.

Michael S. Branicky, Table of n, a(n) for n = 1..45

a(37) and beyond from Michael S. Branicky, Jun 16 2022

A126688 Lowest base in which n has distinct digits.

Original entry on oeis.org

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

Paul Richards, Feb 15 2007

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

			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).

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

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

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A123700 Smallest m such that A123699(m) = n.

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A126688 Lowest base in which n has distinct digits.

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