A257806 -id:A257806 - cp's OEIS frontend

A257803 Positions of odd numbers in A233271, the infinite trunk of inverted binary beanstalk.

1, 4, 7, 9, 12, 17, 18, 21, 23, 24, 25, 27, 30, 34, 35, 38, 41, 42, 49, 52, 53, 54, 55, 57, 60, 64, 65, 68, 70, 73, 74, 75, 76, 77, 81, 82, 83, 90, 93, 95, 96, 103, 106, 107, 108, 109, 111, 114, 118, 119, 122, 127, 128, 131, 132, 134, 136, 137, 138, 139, 140, 145, 147, 148, 149, 150, 151, 155, 156, 157, 164, 167, 168, 171

Offset: 1

Antti Karttunen, May 12 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..7973

Complement: A257804.

Cf. A233271, A257800, A257806, A257807.

Other identities:

For all n >= 1, A257807(a(n)) = n. [A257807 works as a left inverse for this injective function.]

A257804 Positions of even numbers in A233271, the infinite trunk of inverted binary beanstalk.

Original entry on oeis.org

0, 2, 3, 5, 6, 8, 10, 11, 13, 14, 15, 16, 19, 20, 22, 26, 28, 29, 31, 32, 33, 36, 37, 39, 40, 43, 44, 45, 46, 47, 48, 50, 51, 56, 58, 59, 61, 62, 63, 66, 67, 69, 71, 72, 78, 79, 80, 84, 85, 86, 87, 88, 89, 91, 92, 94, 97, 98, 99, 100, 101, 102, 104, 105, 110, 112, 113, 115, 116, 117, 120, 121, 123, 124, 125, 126, 129, 130

Offset: 0

Antti Karttunen, May 12 2015

nonn

We start indexing of this sequence from 0, because a(0) = 0 is a special case, which can be conveniently ignored by considering only the terms from a(1) onward.

Antti Karttunen, Table of n, a(n) for n = 0..8433

Complement: A257803.

Cf. A233271, A257800, A257806, A257808.

Other identities. For all n >= 0:

A257808(a(n)) = n. [A257808 works as a left inverse for this injective function.]

A257807 a(n) = number of odd numbers in range 0 .. n of A233271, the infinite trunk of inverted binary beanstalk.

Original entry on oeis.org

0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7, 8, 8, 9, 10, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 20, 21, 22, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 31, 32, 33, 34, 34, 34, 34, 35, 36, 37, 37, 37, 37, 37, 37, 37, 38

Offset: 0

Antti Karttunen, May 12 2015

nonn

a(0) = 0; and for n >= 1: a(n) = the largest number k such that A257803(k) <= n.

Antti Karttunen, Table of n, a(n) for n = 0..16405

Partial sums of A257800.

Cf. A233271, A257803, A257806, A257808.

a(0) = 0; for n >= 1, a(n) = A257800(n) + a(n-1).
Other identities:
For all n >= 0, a(n) = A257808(n) - A257806(n).
For all n >= 1, a(A257803(n)) = n. [This sequence works as a left inverse of injection A257803.]

A257808 a(n) = number of nonzero even numbers in range 0 .. n of A233271, the infinite trunk of inverted binary beanstalk.

Original entry on oeis.org

0, 0, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 11, 11, 12, 13, 13, 14, 14, 14, 14, 15, 15, 16, 17, 17, 18, 19, 20, 20, 20, 21, 22, 22, 23, 24, 24, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, 32, 32, 32, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 38, 39, 40, 40, 41, 41, 42, 43, 43, 43, 43, 43, 43, 44, 45, 46, 46, 46, 46, 47, 48, 49, 50, 51

Offset: 0

Antti Karttunen, May 12 2015

nonn

a(n) = the largest number k such that A257804(k) <= n.

Antti Karttunen, Table of n, a(n) for n = 0..16405

Cf. A233271, A257800, A257804, A257806, A257807.

a(0) = 0; for n >= 1, a(n) = (1-A257800(n)) + a(n-1).
Other identities. For all n >= 0:
a(n) = A257806(n) + A257807(n).
a(A257804(n)) = n. [This sequence works as a left inverse for injection A257804.]

A260430 Involution of natural numbers: a(1) = 1, a(A257803(1+n)) = A257804(a(n)), a(A257804(n)) = A257803(1+a(n)), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.

Original entry on oeis.org

1, 4, 12, 2, 30, 7, 6, 74, 19, 21, 18, 3, 172, 52, 54, 49, 48, 11, 9, 383, 10, 128, 125, 32, 36, 132, 31, 119, 118, 5, 27, 24, 812, 314, 89, 25, 283, 92, 275, 76, 86, 85, 83, 290, 75, 267, 266, 17, 16, 68, 60, 14, 724, 15, 227, 1675, 219, 659, 207, 51, 64, 599, 216, 61, 232, 583, 174, 50, 204, 210, 201, 193, 208, 8, 45, 40, 1574, 612, 173, 569, 595, 159, 43

Offset: 1

Antti Karttunen, Jul 27 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4453
Index entries for sequences that are permutations of the natural numbers

Cf. A257800, A257803, A257804, A257807, A257808.
Cf. also A233271, A257806.
Related permutations: A260431 - A260434.

a(1) = 1; for n > 1, if A257800(n) = 0 [when n is one of the terms of A257804] a(n) = A257803(1+a(A257808(n))), otherwise [when n is one of the terms of A257803] a(n) = A257804(a(A257807(n)-1)).

A260431 Permutation of natural numbers: a(1) = 1, a(A257804(n)) = 2a(n), a(A257803(1+n)) = 1 + 2a(n), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.

Original entry on oeis.org

1, 2, 4, 3, 8, 6, 5, 16, 9, 12, 10, 7, 32, 18, 24, 20, 17, 13, 14, 64, 11, 36, 33, 19, 25, 48, 21, 40, 34, 15, 26, 28, 128, 65, 37, 22, 72, 49, 66, 38, 41, 35, 50, 96, 42, 80, 68, 30, 27, 52, 56, 29, 129, 23, 73, 256, 67, 130, 74, 39, 44, 144, 98, 51, 97, 132, 76, 43, 82, 81, 70, 100, 69, 31, 53, 57, 257, 192, 84, 160, 131, 75, 45, 136, 60, 54

Offset: 1

Antti Karttunen, Jul 27 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Inverse: A260432.
Related permutations: A260433, A260430, A054429.
Cf. A257800, A257803, A257804, A257807, A257808, A233271.
Cf. also A257806.

a(1) = 1; for n > 1, if A257800(n) = 0 [when n is one of the terms of A257804] a(n) = 2*a(A257808(n)), otherwise [when n is one of the terms of A257803] a(n) = 1 + 2*a(A257807(n)-1).
As a composition of other permutations:
a(n) = A054429(A260433(n)).
a(n) = A260433(A260430(n)).

A260432 Permutation of natural numbers: a(1) = 1, a(2n) = A257804(a(n)), a(2n+1) = A257803(1+a(n)), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.

Original entry on oeis.org

1, 2, 4, 3, 7, 6, 12, 5, 9, 11, 21, 10, 18, 19, 30, 8, 17, 14, 24, 16, 27, 36, 54, 15, 25, 31, 49, 32, 52, 48, 74, 13, 23, 29, 42, 22, 35, 40, 60, 28, 41, 45, 68, 61, 83, 92, 132, 26, 38, 43, 64, 50, 75, 86, 119, 51, 76, 89, 128, 85, 118, 125, 172, 20, 34, 39, 57, 47, 73, 71, 106, 37, 55, 59, 82, 67, 96, 101, 140, 46, 70, 69

Offset: 1

Antti Karttunen, Jul 27 2015

This sequence can be represented as a binary tree. Each left hand child is produced as A257804(n), and each right hand child as A257803(1+n), when the parent contains n:
                                     |
                  ...................1...................
                 2                                       4
       3......../ \........7                   6......../ \........12
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
   5       9          11       21         10       18         19       30
  8 17   14 24      16  27   36  54     15  25   31  49     32  52   48  74
etc.

Antti Karttunen, Table of n, a(n) for n = 1..8191
Index entries for sequences that are permutations of the natural numbers

Inverse: A260431.
Related permutations: A260434, A260430, A054429.
Cf. A257803, A257804, A257807, A257808.
Cf. also A233271, A257806.

a(1) = 1, a(2n) = A257804(a(n)), a(2n+1) = A257803(1+a(n)).
As a composition of other permutations:
a(n) = A260434(A054429(n)).
a(n) = A260430(A260434(n)).

A260434 Permutation of natural numbers: a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.

Original entry on oeis.org

1, 4, 2, 12, 6, 7, 3, 30, 19, 18, 10, 21, 11, 9, 5, 74, 48, 52, 32, 49, 31, 25, 15, 54, 36, 27, 16, 24, 14, 17, 8, 172, 125, 118, 85, 128, 89, 76, 51, 119, 86, 75, 50, 64, 43, 38, 26, 132, 92, 83, 61, 68, 45, 41, 28, 60, 40, 35, 22, 42, 29, 23, 13, 383, 314, 275, 219, 266, 208, 201, 152, 283, 227, 207, 159, 174, 129, 127, 88

Offset: 1

Antti Karttunen, Jul 27 2015

This sequence can be represented as a binary tree. Each left hand child is produced as A257803(1+n), and each right hand child as A257804(n), when the parent contains n:
                                     |
                  ...................1...................
                 4                                       2
      12......../ \........6                   7......../ \........3
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  30       19         18       10         21       11          9       5
74  48   52  32     49  31   25  15     54  36   27  16      24 14   17 8
etc.
Note how this is a mirror image of the tree shown in A260432.

Antti Karttunen, Table of n, a(n) for n = 1..16383
Index entries for sequences that are permutations of the natural numbers

Inverse: A260433.
Related permutations: A260432, A260430, A054429.
Cf. A257803, A257804, A257807, A257808.
Cf. also A233271, A257806.

a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)).
As a composition of other permutations:
a(n) = A260432(A054429(n)).
a(n) = A260430(A260432(n)).

A257805 Partial sums of A257259: a(0) = 1; for n >= 1, a(n) = A257259(n) + a(n-1).

Original entry on oeis.org

1, 0, 0, -1, -2, -5, -6, -12, -20, -30, -37, -41, -39, -37, -51, -141, -459, -1355, -3521, -8212, -17510, -34685, -64692, -114953, -196617, -326254, -527227, -828432, -1254932, -1800115, -2361626, -2613748, -1777205, 1765725, 11078200, 31587185, 72445272, 148564309, 283768148, 516004565, 906713910, 1559424960, 2660917133, 4581930804, 8140743021, 15311144248, 31111188060, 68512065476

Offset: 0

Antti Karttunen, May 13 2015

sign

Cf. A218600, A257259, A257806.

Cf. also A218542, A218543 and A218789.

a(0) = 1; for n >= 1, a(n) = A257259(n) + A257805(n-1).
Other identities. For all n >= 0:
a(n) = -A257806(A218600(n+1)).

A260433 Permutation of natural numbers: a(1) = 1, a(A257803(1+n)) = 2a(n), a(A257804(n)) = 1 + 2a(n), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.

Original entry on oeis.org

1, 3, 7, 2, 15, 5, 6, 31, 14, 11, 13, 4, 63, 29, 23, 27, 30, 10, 9, 127, 12, 59, 62, 28, 22, 47, 26, 55, 61, 8, 21, 19, 255, 126, 58, 25, 119, 46, 125, 57, 54, 60, 45, 95, 53, 111, 123, 17, 20, 43, 39, 18, 254, 24, 118, 511, 124, 253, 117, 56, 51, 239, 93, 44, 94, 251, 115, 52, 109, 110, 121, 91, 122, 16, 42, 38, 510, 191, 107, 223, 252, 116, 50, 247, 35, 41

Offset: 1

Antti Karttunen, Jul 27 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences that are permutations of the natural numbers

Inverse: A260434.
Related permutations: A260431, A260430, A054429.
Cf. A257800, A257803, A257804, A257807, A257808.
Cf. also A233271, A257806.

a(1) = 1; for n > 1, if A257800(n) = 0 [when n is one of the terms of A257804] a(n) = 1 + 2*a(A257808(n)), otherwise [when n is one of the terms of A257803] a(n) = 2*a(A257807(n)-1).
As a composition of other permutations:
a(n) = A054429(A260431(n)).
a(n) = A260431(A260430(n)).

cp's OEIS Frontend

A257803 Positions of odd numbers in A233271, the infinite trunk of inverted binary beanstalk.

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A257804 Positions of even numbers in A233271, the infinite trunk of inverted binary beanstalk.

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A257807 a(n) = number of odd numbers in range 0 .. n of A233271, the infinite trunk of inverted binary beanstalk.

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A257808 a(n) = number of nonzero even numbers in range 0 .. n of A233271, the infinite trunk of inverted binary beanstalk.

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Formula

A260430 Involution of natural numbers: a(1) = 1, a(A257803(1+n)) = A257804(a(n)), a(A257804(n)) = A257803(1+a(n)), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.

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Author

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Crossrefs

Formula

A260431 Permutation of natural numbers: a(1) = 1, a(A257804(n)) = 2*a(n), a(A257803(1+n)) = 1 + 2*a(n), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.

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Author

Keywords

Links

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Formula

A260432 Permutation of natural numbers: a(1) = 1, a(2n) = A257804(a(n)), a(2n+1) = A257803(1+a(n)), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.

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Author

Keywords

Comments

Links

Crossrefs

Formula

A260434 Permutation of natural numbers: a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.

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Comments

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Crossrefs

Formula

A257805 Partial sums of A257259: a(0) = 1; for n >= 1, a(n) = A257259(n) + a(n-1).

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A260433 Permutation of natural numbers: a(1) = 1, a(A257803(1+n)) = 2*a(n), a(A257804(n)) = 1 + 2*a(n), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.

Views

Author

Keywords

Links

Crossrefs

Formula

A260431 Permutation of natural numbers: a(1) = 1, a(A257804(n)) = 2a(n), a(A257803(1+n)) = 1 + 2a(n), where A257804 and A257803 give the positions of even and odd terms in A233271, the infinite trunk of inverted binary beanstalk.

A260433 Permutation of natural numbers: a(1) = 1, a(A257803(1+n)) = 2a(n), a(A257804(n)) = 1 + 2a(n), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk.