cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A023800 Xenodromes: all digits in base 5 are different.

Original entry on oeis.org

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A023798 - A023810.

Programs

  • Maple
    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
  • Mathematica
    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

Views

Author

Olivier Gérard

Keywords

Comments

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

Examples

			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

Links

Crossrefs

All three of A023805, A160453, A168186 are different.

Programs

  • Mathematica
    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

Views

Author

Olivier Gérard

Keywords

Examples

			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.

Links

Crossrefs

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

Programs

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

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A023798 - A023810.

Programs

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

A369635 Numbers in whose base 3-representation every two consecutive digits and every three consecutive digits are distinct.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 11, 15, 19, 21, 34, 46, 59, 65, 102, 140, 177, 202, 308, 420, 532, 606, 925, 1261, 1598, 1820, 2775, 3785, 4794, 5467, 8327, 11355, 14383, 16401, 24982, 34066, 43151, 49205, 74946, 102200, 129453, 147622, 224840, 306600, 388360, 442866
Offset: 1

Views

Author

Clark Kimberling, Feb 26 2024

Keywords

Comments

In other words, the ternary expansion of the number does not contain any string xx or xxx.
The first eleven terms of this sequence comprise the base-3 xenodrome, A023798.
Ordered union of {0}, A037496, A037504, A037512, and A037520.

Examples

			The base-3 representation of 7 is 21, in which every two consecutive digits are distinct, so 7 is a term of the sequence.
The base-3 representation of 532 is 201201, in which every 3 consecutive digits are distinct, so 532 is a term of the sequence.

Crossrefs

Cf. A023798, A037496, A037504, A037512, and A037520.

Programs

  • Mathematica
    s1 = LinearRecurrence[{3, 0, 1, -3}, {0, 1, 3, 11}, 30]  (* A037496 *)
s2 = LinearRecurrence[{3, 0, 1, -3}, {0, 1, 5, 15}, 30]  (* A037504 *)
s3 = LinearRecurrence[{3, 0, 1, -3}, {0, 2, 6, 19}, 30]  (* A037512 *)
s4 = LinearRecurrence[{3, 0, 1, -3}, {0, 7, 21, 65}, 30] (* A037520 *)
s = Union[s1, s2, s3, s4]
Showing 1-5 of 5 results.

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