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

Author

Rémy Sigrist, May 11 2020

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A003188, A163332.

Programs

PARI

a(n) = { for (k=1, oo, if (n