Rémy Sigrist, <a href="/A376674/b376674_1.txt">Table of n, a(n) for n = 1..10048</a>

proposed

approved

editing

proposed

Rémy Sigrist, <a href="/A376674/a376674.gp.txt">PARI program</a>

Rémy Sigrist, <a href="/A376674/a376674.gp.txt">PARI program</a>

Rémy Sigrist, <a href="/A376674/b376674_1.txt">Table of n, a(n) for n = 1..10048</a>

Rémy Sigrist, <a href="/A376674/a376674.gp.txt">PARI program</a>

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

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

Cf. A351653, A376637.

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.

allocated for Rémy Sigrist

a(n) is the unique number k 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

1,1

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

<a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

(PARI) \\ See Links section.

Cf. A376637.

allocated

nonn,base

Rémy Sigrist, Oct 01 2024

approved

editing

allocated for Rémy Sigrist

allocated

approved