A334792 Let L_0 = (0, 1, 2, ...); for k = 1, 2, ..., L_k is obtained by splitting L_{k-1} into runs of k! terms and reversing even-indexed runs; {a(n)} is the limit of L_k as k tends to infinity.

0, 1, 3, 2, 4, 5, 10, 11, 9, 8, 6, 7, 12, 13, 15, 14, 16, 17, 22, 23, 21, 20, 18, 19, 43, 42, 44, 45, 47, 46, 41, 40, 38, 39, 37, 36, 31, 30, 32, 33, 35, 34, 29, 28, 26, 27, 25, 24, 48, 49, 51, 50, 52, 53, 58, 59, 57, 56, 54, 55, 60, 61, 63, 62, 64, 65, 70, 71

Offset

0,3

Comments

A003188 can be obtained in the same manner by considering runs of 2^k terms.

A163332 can be obtained in the same manner by considering runs of 3^k terms.

This sequence is a permutation of the nonnegative integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..5039 (n = 0..7!-1)

Index entries for sequences that are permutations of the natural numbers

Example

L_0 = (0, 1, 2, 3, 4, 5, ...)
L_1 = (0, 1, 2, 3, 4, 5, ...)
L_2 = (0, 1, 3, 2, 4, 5, ...)
As 5 < k! for k > 2, we have:
- a(0) = 0,
- a(1) = 1,
- a(2) = 3,
- a(3) = 2,
- a(4) = 4,
- a(5) = 5.

Prog

(PARI) a(n) = { for (k=1, oo, if (n<k!, while (k, my (q=n\k!, r=n%k!); if (q%2, n=(q+1)*k!-1-r; ); k--); return (n))) }

Crossrefs

Cf. A003188, A163332.

Sequence in context: A211363 A376901 A059320 * A255167 A264993 A280318

Adjacent sequences: A334789 A334790 A334791 * A334793 A334794 A334795

Keyword

nonn

Author

Rémy Sigrist, May 11 2020

Status

approved