A376674 a(n) is the unique number k different from n such that the words A376637(n) and A376637(k) have the same run lengths transform.

2, 1, 6, 5, 4, 3, 10, 9, 8, 7, 16, 15, 14, 13, 12, 11, 24, 23, 22, 21, 20, 19, 18, 17, 28, 27, 26, 25, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 48, 47, 46, 45, 44, 43, 42, 41, 56, 55, 54, 53, 52, 51, 50, 49, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58

Offset: 1

Author

Rémy Sigrist, Oct 01 2024

Keywords

• nonn
• base

Comments

Also, replacing 1's by 2's and 2's by 1's in A376637(n) yields A376637(a(n)).

This sequence is a self-inverse permutation of the positive integers without fixed points.

Examples

			The first terms, alongside the corresponding terms from A376637 and their run lengths transform, are:
  n   a(n)  A376637(n)  A376637(a(n))  RL
  --  ----  ----------  -------------  ---
   1     2           1              2    1
   2     1           2              1    1
   3     6          11             22    2
   4     5          12             21   11
   5     4          21             12   11
   6     3          22             11    2
   7    10         112            221   21
   8     9         122            211   12
   9     8         211            122   12
  10     7         221            112   21
  11    16        1121           2212  211
  12    15        1122           2211   22
  13    14        1211           2122  112
  14    13        2122           1211  112
  15    12        2211           1122   22
  16    11        2212           1121  211
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10048
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A351653, A376637.

Programs

PARI

\\ See Links section.

Formula

A351653(A376637(a(n))) = A351653(A376637(n)).