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 1-4 of 4 results.

A263327 A permutation of {0, 1, ..., 1023} corresponding to lexicographical ordering A262557 of numbers with decreasing digits A009995.

Original entry on oeis.org

0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 3, 5, 6, 9, 10, 12, 17, 18, 20, 24, 33, 34, 36, 40, 48, 65, 66, 68, 72, 80, 96, 129, 130, 132, 136, 144, 160, 192, 257, 258, 260, 264, 272, 288, 320, 384, 513, 514, 516, 520, 528, 544, 576, 640, 768, 7, 11, 13, 14
Offset: 0

Views

Author

Reinhard Zumkeller, Oct 15 2015

Keywords

Comments

For n = 1..1023, A262557(a(n)) = A009995(n).
Cycle type = (1^12, 3^2, 10^2, 74, 912), i.e., this permutation has 12 fixed points, two 3-cycles and two 10-cycles, and two more cycles of length 74 and 912. See A263355 for the list of these cycles, A263383 for the length of the n-th cycle (ordered by increasing largest element).

Crossrefs

Cf. A009995, A262557, A263328 (inverse), A263329 (fixed points), A263383, A263355 (cycles).
Row 10 of A294648.

Programs

  • Haskell
    a263327 0 = 0
    a263327 n = head [x | x <- [1..1023], a262557 x == a009995' n]
    
  • Mathematica
    SortBy[Range[0, 1023], DigitCount[#, 2, 1] &] (* Paolo Xausa, Mar 31 2025 *)
  • PARI
    A263327=vecsort(A262557,,1) \\ Does not include a(0)=0. - M. F. Hasler, Dec 11 2019

Extensions

Edited by M. F. Hasler, Dec 11 2019

A263328 Permutation of {0, ..., 1023} corresponding to lexicographic ordering of numbers with decreasing digits (A009995). Inverse of A263327.

Original entry on oeis.org

0, 1, 2, 11, 3, 12, 13, 56, 4, 14, 15, 57, 16, 58, 59, 176, 5, 17, 18, 60, 19, 61, 62, 177, 20, 63, 64, 178, 65, 179, 180, 386, 6, 21, 22, 66, 23, 67, 68, 181, 24, 69, 70, 182, 71, 183, 184, 387, 25, 72, 73, 185, 74, 186, 187, 388, 75, 188, 189, 389, 190
Offset: 0

Views

Author

Reinhard Zumkeller, Oct 15 2015

Keywords

Comments

For n = 1..1023: A009995(a(n)) = A262557(n).
The fixed points and cycles of this permutation (up to reversal the same as for its inverse A263327) are listed in A263355. - M. F. Hasler, Dec 11 2019

Crossrefs

Cf. A009995, A262557, A263327 (inverse), A263329 (fixed points).

Programs

  • Haskell
    a263328 0 = 0
    a263328 n = head [x | x <- [1..1023], a009995' x == a262557 n]
    
  • PARI
    A263328=vecsort(A263327,,1) \\ Does not include a(0)=0. - M. F. Hasler, Dec 11 2019

A263329 Fixed points of permutations A263327 and A263328.

Original entry on oeis.org

0, 1, 2, 17, 18, 84, 939, 1005, 1006, 1021, 1022, 1023
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 15 2015

Keywords

Comments

a(k) = A263355(k,1) for k such that A263383(k) = 1.

Crossrefs

Programs

  • Haskell
    a263329 n = a263329_list !! (n-1)
    a263329_list = [x | x <- [0..1023], a263327 x == x]

A263383 Lengths of cycles of permutation A263327.

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 1, 10, 1, 74, 1, 1, 10, 3, 912, 1, 1, 1
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 16 2015

Keywords

Comments

Cycle type of permutation A263327 = (1^12, 3^2, 10^2, 74, 912);
A263355(k,1) = A263329(k) for k such that a(k) = 1.
row lengths of A263355;
number of terms = 18; sum of terms = 1024.

Examples

			See A263355.
		

Crossrefs

Programs

  • Haskell
    a263383 = length . a263355_row
Showing 1-4 of 4 results.