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

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

Author

Reinhard Zumkeller, Oct 15 2015

Keywords

• nonn
• fini
• full

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).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1023

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