A351653 -id:A351653 - cp's OEIS frontend

A376676 a(n) is the unique k such that the run lengths transform of A376637(n) equals A376637(k).

1, 1, 2, 3, 3, 2, 5, 4, 4, 5, 9, 6, 7, 7, 6, 9, 10, 11, 8, 13, 13, 8, 11, 10, 15, 12, 12, 15, 14, 21, 16, 17, 19, 18, 18, 19, 17, 16, 21, 14, 23, 22, 24, 20, 20, 24, 22, 23, 27, 28, 25, 26, 26, 25, 28, 27, 38, 30, 29, 34, 33, 32, 32, 33, 34, 29, 30, 38, 37, 36

Offset: 1

Rémy Sigrist, Oct 01 2024

Every positive integer appears twice in this sequence.

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

Rémy Sigrist, Table of n, a(n) for n = 1..10048
Rémy Sigrist, PARI program

Cf. A351653, A376637, A376698, A376733.

PARI
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\\ See Links section.
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A376637(a(n)) = A351653(A376637(n)).

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.

Original entry on oeis.org

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

Rémy Sigrist, Oct 01 2024

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.

			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

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

Cf. A351653, A376637.

PARI
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\\ See Links section.
```

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

cp's OEIS Frontend

A376676 a(n) is the unique k such that the run lengths transform of A376637(n) equals A376637(k).

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