A023810 -id:A023810 - cp's OEIS frontend

A023800 Xenodromes: all digits in base 5 are different.

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 27, 28, 29, 35, 38, 39, 40, 42, 44, 45, 47, 48, 51, 53, 54, 55, 58, 59, 65, 66, 69, 70, 71, 73, 76, 77, 79, 80, 82, 84, 85, 86, 89, 95, 96, 97, 101, 102, 103, 105, 107, 108, 110, 111, 113

Offset: 1

Olivier Gérard

Nathaniel Johnston, Table of n, a(n) for n = 1..261 (full sequence)

Cf. A023798 - A023810.

A023800 := proc(n) option remember: local d,j,k,inseq: if(n=1)then return 0:fi: for k from procname(n-1)+1 do d:=convert(k,base,5): inseq:=true: for j from 0 to 4 do if(numboccur(d,j)>=2)then inseq:=false:break: fi: od: if(inseq)then return k: fi: od: end: seq(A023800(n),n=1..66); # Nathaniel Johnston, May 17 2011

Select[Range[0, 3000], Length[b5 = IntegerDigits[#, 5]] == Length[Union[b5]]&] (* Jean-François Alcover, Feb 13 2014 *)
Select[Range[0,120],Max[DigitCount[#,5]]==1&] (* Harvey P. Dale, Sep 22 2016 *)

A023805 Xenodromes: all digits in base 11 are different.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74

Offset: 1

Olivier Gérard

Considering some base b, there are b numbers with 1 digit, (b-1)*(b-1) numbers with 2 digits -- since leading 0's are not allowed and the second digit must avoid the first. There are (b-1)*(b-1)*(b-2) numbers with 3 digits, (b-1)*(b-1)*(b-2)*..*(b-d+1) numbers with d digits, in total b+(b-1)*sum_{d=2..b} (b-1)!/(b-d)! = b+(b-1)^2* 2F0(1,2-b;;-1) = A001339(b-1). The formula is applicable to sequences A023798 - A023810. This sequence here as A001339(11-1) = 98641011 terms. [From R. J. Mathar, Jan 27 2010]

Last term is a(98641011) = 282458553905. - Charles R Greathouse IV, Jun 16 2012

			121 (in decimal) = 100 (base 11) is a member of A168186 but not a member of this sequence. - Robert Munafo, Jan 26 2010
156 is in A023805 but not in A168186. - Franklin T. Adams-Watters, Jan 26 2010

Paolo Xausa, Table of n, a(n) for n = 1..10000

All three of A023805, A160453, A168186 are different.

Select[Range[0, 100], Max[DigitCount[#, 11]] == 1 &] (* Paolo Xausa, Mar 22 2025 *)

A023802 Xenodromes: all digits in base 7 are different.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 51, 52, 53, 54, 55, 63, 66, 67, 68, 69, 70, 72, 74, 75, 76, 77, 79, 80, 82, 83, 84, 86, 87, 88, 90

Offset: 1

Olivier Gérard

			4146 in base 7 is 15042. Since no two digits of the base 7 representation are the same, 4146 is in the sequence.
4147 in base 7 is 15043. Since no two digits of the base 7 representation are the same, 4147 is in the sequence.
4148 in base 7 is 15044. Since the digit 4 appears twice in the base 7 representation, 4148 is not in the sequence.

Nathaniel Johnston, Table of n, a(n) for n = 1..11743 (full sequence)

Cf. A023798 - A023810.
Cf. A007093 (numbers in base 7).
Cf. A044956 (includes a subset of the complement of this sequence).

Select[Range[0, 97], Max[DigitCount[#, 7]] == 1 &] (* Alonso del Arte, Feb 09 2019 *)

isok(n) = my(d=digits(n, 7)); #d == #Set(d); \\ Michel Marcus, Feb 09 2019

A023801 Xenodromes: numbers such that all digits in base 6 are different.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 38, 39, 40, 41, 48, 51, 52, 53, 54, 56, 58, 59, 60, 62, 63, 65, 66, 68, 69, 70, 73, 75, 76, 77, 78, 81, 82, 83, 90, 91, 94, 95, 96, 97, 99, 101, 102

Offset: 1

Olivier Gérard

Nathaniel Johnston, Table of n, a(n) for n = 1..1631 (full sequence)

Cf. A023798 - A023810.

Select[Range[0, 150], Max[DigitCount[#, 6]] == 1 &] (* Paolo Xausa, Mar 22 2025 *)

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A023800 Xenodromes: all digits in base 5 are different.

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A023805 Xenodromes: all digits in base 11 are different.

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A023802 Xenodromes: all digits in base 7 are different.

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A023801 Xenodromes: numbers such that all digits in base 6 are different.

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