A331851 -id:A331851 - cp's OEIS frontend

A331855 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.

1, 1, 2, 1, 3, 3, 3, 1, 4, 6, 5, 4, 5, 4, 4, 1, 5, 10, 9, 9, 8, 8, 9, 5, 7, 9, 8, 5, 7, 5, 5, 1, 6, 15, 14, 16, 12, 16, 18, 12, 11, 16, 13, 12, 15, 13, 14, 6, 9, 16, 15, 13, 13, 12, 12, 6, 10, 12, 11, 6, 9, 6, 6, 1, 7, 21, 20, 25, 18, 27, 30, 22, 16, 27, 25

Offset: 0

Rémy Sigrist, Jan 29 2020

			For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
      "110" -> "011" -> 3
      "1" and "10" -> "1" and "01" -> 5
      "11" and "0" -> "11" and "0" -> 6
      "1" and "1" and "0" -> "1" and "1" and "0" -> 6
- we have 3 distinct values,
- hence a(6) = 3.

Rémy Sigrist, Table of n, a(n) for n = 0..16384
Rémy Sigrist, PARI program for A331855
Index entries for sequences related to binary expansion of n

See A331851 for similar sequences.
See A331856 and A331857 for the least and greatest values, respectively.
Cf. A000096, A000217.

PARI
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See Links section.
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a(2^k-1) = 1 for any k >= 0.
a(2^k) = k+1 for any k >= 0.
a(2^k+1) = A000217(k) for any k > 0.
a(2^k+2) = A000096(k-1) for any k > 3.
a(2^k+3) = (k-1)^2 for any k > 1.

A331852 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise XOR operator to the numbers represented by the blocks.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 9, 9, 10, 10, 9, 9, 10, 10, 11, 11, 11, 11, 9, 9, 8, 8, 7, 7, 10, 10, 10, 10, 11, 11, 10, 10, 11, 11, 11, 11, 12

Offset: 0

Rémy Sigrist, Jan 29 2020

			For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
      "110" -> 6
      "1" and "10" -> 1 XOR 2 = 3
      "11" and "0" -> 3 XOR 0 = 3
      "1" and "1" and "0" -> 1 XOR 1 XOR 0 = 0
- we have 3 distinct values,
- hence a(6) = 3.

Rémy Sigrist, PARI program for A331852
Index entries for sequences related to binary expansion of n

See A331851 for similar sequences.

Cf. A038348.

PARI
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See Links section.
```

a(2^k) = k+1 for any k >= 0.

Apparently a(2^k-1) = A038348(k) for any k >= 0.

A331853 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise AND operator to the numbers represented by the blocks.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 2, 2, 2, 3, 3, 4, 2, 3, 3, 3, 2, 3, 3, 4, 2, 3, 3, 4, 2, 3, 3, 5, 2, 3, 3, 3, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 6, 2, 3, 3, 5, 3, 4, 4, 5, 2, 3, 3, 5, 3, 4, 4, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 6, 2, 3, 3, 4, 3, 4, 4

Offset: 0

Rémy Sigrist, Jan 29 2020

			For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
      "110" -> 6
      "1" and "10" -> 1 AND 2 = 0
      "11" and "0" -> 3 AND 0 = 0
      "1" and "1" and "0" -> 1 AND 1 AND 0 = 0
- we have 2 distinct values,
- hence a(6) = 2.

Rémy Sigrist, PARI program for A331853
Index entries for sequences related to binary expansion of n

See A331851 for similar sequences.

Cf. A008619.

PARI
```
See Links section.
```

a(2^k) = 2 for any k > 0.

a(2^k-1) = A008619(k+1) for any k >= 0.

A331854 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise OR operator to the numbers represented by the blocks.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 4, 5, 5, 4, 4, 5, 5, 7, 6, 7, 6, 7, 6, 7, 7, 8, 7, 7, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 8, 9, 8, 9, 7, 10, 9, 9, 8, 9, 9, 11, 10, 10, 9, 11, 10, 11, 11, 11, 10, 9, 9, 6, 6, 7, 7, 11, 10, 12, 10, 12, 11, 12, 10, 14, 10, 13, 11, 11

Offset: 0

Rémy Sigrist, Jan 29 2020

			For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
      "110" -> 6
      "1" and "10" -> 1 OR 2 = 3
      "11" and "0" -> 3 OR 0 = 3
      "1" and "1" and "0" -> 1 OR 1 OR 0 = 1
- we have 3 distinct values,
- hence a(6) = 3.

Rémy Sigrist, PARI program for A331854
Index entries for sequences related to binary expansion of n

See A331851 for similar sequences.

PARI
```
See Links section.
```

a(2^k) = k+1 for any k >= 0.

a(2^k-1) = k for any k > 0.

cp's OEIS Frontend

A331855 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.

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A331852 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise XOR operator to the numbers represented by the blocks.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A331853 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise AND operator to the numbers represented by the blocks.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A331854 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise OR operator to the numbers represented by the blocks.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula