A269838 -id:A269838 - cp's OEIS frontend

A355405 Inverse permutation to A269838.

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 17, 11, 33, 18, 13, 12, 65, 14, 129, 20, 19, 34, 257, 16, 21, 66, 15, 25, 513, 22, 1025, 24, 35, 130, 37, 23, 2049, 258, 67, 26, 4097, 38, 8193, 36, 29, 514, 16385, 27, 41, 42, 131, 68, 32769, 30, 49, 40, 259, 1026

Offset: 1

Rémy Sigrist, Jul 01 2022

nonn

			A269838(38) = 42, so a(42) = 38.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A269838.

PARI
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See Links section.
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a(prime(n)) = 2^(n-1) + 1 (where prime(n) denotes the n-th prime number).

A355435 Lexicographically earliest sequence of distinct positive integers such that for any n > 1, a(n) is a multiple of a(A080079(n-1)).

Original entry on oeis.org

1, 2, 4, 3, 6, 8, 10, 5, 15, 20, 16, 12, 9, 24, 14, 7, 21, 28, 48, 18, 36, 32, 40, 30, 25, 50, 56, 42, 27, 44, 22, 11, 33, 66, 88, 54, 84, 112, 100, 75, 60, 80, 64, 72, 90, 96, 140, 63, 35, 70, 120, 45, 108, 128, 160, 105, 55, 110, 104, 78, 39, 52, 26, 13

Offset: 1

Rémy Sigrist, Jul 02 2022

This sequence is a permutation of the positive integers with inverse A355436.
The construction of this sequence is similar to that of A269838.
This sequence can also be seen as an irregular table:
- with row lengths given by A011782,
- with initial row (1),
- given the first k+1 rows (with globally 2^k terms), the next row contains a multiple of a(2^k), followed by a multiple of a(2^k-1), ..., followed by a multiple of a(1).

			As an irregular table, the first rows are:
    [1]
    [2]
    [4, 3]
    [6, 8, 10, 5]
    [15, 20, 16, 12, 9, 24, 14, 7]
    [21, 28, 48, 18, 36, 32, 40, 30, 25, 50, 56, 42, 27, 44, 22, 11]
.
The first terms are:
  n   a(n)  A080079(n-1)  a(A080079(n-1))
  --  ----  ------------  ---------------
   1     1  N/A           N/A
   2     2             1                1
   3     4             2                2
   4     3             1                1
   5     6             4                3
   6     8             3                4
   7    10             2                2
   8     5             1                1
   9    15             8                5
  10    20             7               10
  11    16             6                8
  12    12             5                6
  13     9             4                3
  14    24             3                4
  15    14             2                2
  16     7             1                1

Rémy Sigrist, Table of n, a(n) for n = 1..8192
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A011782, A080079, A269838, A355436 (inverse).

PARI
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See Links section.
```

a(2^n) = prime(n) for any n > 0 (where prime(n) denotes the n-th prime number).

cp's OEIS Frontend

A355405 Inverse permutation to A269838.

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