A044918 -id:A044918 - cp's OEIS frontend

A280504 a(n) = A280500(n,A280503(n)).

1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 11, 1, 13, 7, 1, 8, 1, 9, 19, 10, 1, 11, 13, 6, 25, 13, 1, 7, 11, 15, 1, 16, 1, 15, 13, 2, 37, 1, 11, 12, 41, 1, 25, 22, 1, 13, 47, 4, 11, 25, 1, 1, 19, 3, 55, 1, 13, 11, 59, 5, 61, 31, 1, 32, 1, 33, 67, 34, 69, 35, 61, 36, 1, 37, 13, 38, 59, 39, 25, 40, 81, 41, 11, 42, 1, 43, 87, 44, 55, 45, 91, 46, 1, 47, 19, 24, 97, 49, 1, 25, 13

Offset: 1

Antti Karttunen, Jan 09 2017

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences related to binary expansion of n

Cf. A048720, A056539, A280500, A280503, A280506.

Cf. A044918 (very likely gives the positions of all ones).

(define (A280504 n) (A280500bi n (A280503 n))) ;; Code for A280500bi given in A280500.

a(n) = A280500(n,A280503(n)).
Other identities. For all n >= 1:
A048720(a(n), A280503(n)) = n.

A357522 Reverse run lengths in binary expansions of terms of A063037: for n >= 0, a(n) is the unique k such that A063037(1+k) = A056539(A063037(1+n)).

Original entry on oeis.org

0, 1, 2, 3, 6, 5, 4, 7, 8, 11, 10, 9, 16, 17, 18, 15, 12, 13, 14, 19, 32, 23, 22, 21, 24, 31, 28, 27, 26, 29, 30, 25, 20, 33, 42, 49, 48, 43, 44, 47, 50, 41, 34, 37, 38, 53, 52, 39, 36, 35, 40, 51, 46, 45, 74, 75, 84, 65, 58, 59, 64, 85, 86, 63, 60, 57, 66, 83

Offset: 0

Rémy Sigrist, Oct 02 2022

This sequence is a self-inverse permutation of the nonnegative integers.

			For n = 42:
- A063037(1+42) = 86,
- the binary expansion of 86 is "1010110",
- reversing run lengths yields "1001010",
- this corresponds to 74 = A063037(1+34),
- hence a(42) = 34.

Rémy Sigrist, Table of n, a(n) for n = 0..10944
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

See A357523 for a similar sequence.

Cf. A044918, A056539, A063037.

PARI
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See Links section.
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a(n) = n iff n = 0 or A044813(1+n) belongs to A044918.

A357523 Reverse run lengths in binary expansions of terms of A166535: for n > 0, a(n) is the unique k such that A166535(k) = A056539(A166535(n)); a(0) = 0.

Original entry on oeis.org

0, 1, 2, 3, 6, 5, 4, 7, 14, 9, 10, 13, 12, 11, 8, 15, 20, 23, 24, 19, 16, 27, 26, 17, 18, 25, 22, 21, 40, 41, 46, 35, 32, 49, 50, 31, 36, 45, 42, 39, 28, 29, 38, 43, 44, 37, 30, 51, 48, 33, 34, 47, 88, 63, 62, 89, 94, 57, 68, 83, 80, 71, 54, 53, 72, 79, 84, 67

Offset: 0

Rémy Sigrist, Oct 02 2022

This sequence is a self-inverse permutation of the nonnegative integers.

			For n = 42:
- A166535(42) = 50,
- the binary expansion of 50 is "110010",
- reversing run lengths yields "101100",
- this corresponds to 44 = A166535(38),
- hence a(42) = 38.

Rémy Sigrist, Table of n, a(n) for n = 0..12639
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

See A357522 for a similar sequence.

Cf. A044918, A056539, A166535.

PARI
```
See Links section.
```

a(n) = n iff n = 0 or A166535(n) belongs to A044918.

A357527 Reverse run lengths in binary expansions of terms of A044813: for n > 0, a(n) is the unique k such that A044813(k) = A056539(A044813(n)); a(0) = 0.

Original entry on oeis.org

0, 1, 2, 4, 3, 5, 7, 6, 8, 12, 11, 10, 9, 13, 23, 18, 20, 22, 15, 21, 16, 19, 17, 14, 24, 36, 29, 33, 35, 26, 34, 32, 31, 27, 30, 28, 25, 37, 55, 44, 47, 49, 52, 54, 39, 53, 51, 40, 50, 41, 48, 46, 42, 45, 43, 38, 56, 82, 63, 68, 76, 79, 81, 58, 69, 73, 80, 78

Offset: 0

Rémy Sigrist, Oct 02 2022

This sequence is a self-inverse permutation of the nonnegative integers.

			For n = 42:
- A044813(42) = 159,
- the binary expansion of 159 is "10011111",
- reversing run lengths yields "11111001",
- this corresponds to 249 = A044813(52),
- hence a(42) = 52.

Rémy Sigrist, Table of n, a(n) for n = 0..11666
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

See A057164, A357522 and A357523 for similar sequences.

Cf. A044813, A044918, A056539.

PARI
```
See Links section.
```

a(n) = n iff n = 0 or A044813(n) belongs to A044918.

A357530 Reverse run lengths in binary expansions of terms of A031443: for n > 0, a(n) is the unique k such that A031443(k) = A056539(A031443(n)); a(0) = 0.

Original entry on oeis.org

0, 1, 2, 3, 4, 11, 8, 7, 6, 9, 12, 5, 10, 13, 14, 45, 41, 31, 18, 38, 28, 21, 22, 27, 37, 36, 26, 23, 20, 29, 39, 17, 32, 42, 46, 35, 25, 24, 19, 30, 40, 16, 33, 43, 47, 15, 34, 44, 48, 49, 170, 165, 150, 115, 54, 161, 146, 111, 58, 136, 101, 68, 81, 88, 123

Offset: 0

Rémy Sigrist, Oct 02 2022

This sequence is a self-inverse permutation of the nonnegative integers.

			For n = 42:
- A031443(42) = 210,
- the binary expansion of 210 is "11010010",
- reversing run lengths yields "10110100",
- this corresponds to 180 = A031443(33),
- hence a(42) = 33.

Rémy Sigrist, Table of n, a(n) for n = 0..8788
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

See A057164 for a similar sequence.

Cf. A031443, A044918, A056539.

PARI
```
See Links section.
```

a(n) = n iff n = 0 or A031443(n) belongs to A044918.

cp's OEIS Frontend

A280504 a(n) = A280500(n,A280503(n)).

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A357522 Reverse run lengths in binary expansions of terms of A063037: for n >= 0, a(n) is the unique k such that A063037(1+k) = A056539(A063037(1+n)).

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A357523 Reverse run lengths in binary expansions of terms of A166535: for n > 0, a(n) is the unique k such that A166535(k) = A056539(A166535(n)); a(0) = 0.

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A357527 Reverse run lengths in binary expansions of terms of A044813: for n > 0, a(n) is the unique k such that A044813(k) = A056539(A044813(n)); a(0) = 0.

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A357530 Reverse run lengths in binary expansions of terms of A031443: for n > 0, a(n) is the unique k such that A031443(k) = A056539(A031443(n)); a(0) = 0.

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