A355904 -id:A355904 - cp's OEIS frontend

A355913 Negasemiternary (or NST) representation of the unit ambinumber (1,0).

2, 1, 1, 2, 0, 1, 0, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 0, 2, 1, 2, 1, 2, 2, 0, 2, 0, 1, 0, 2, 1, 2, 1, 0, 0, 2, 2, 0, 1, 1, 1, 0, 1, 1, 0, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 1, 2, 1, 2, 0, 1, 2

Offset: 1

N. J. A. Sloane, Sep 19 2022

nonn

			(1, 0) = 2.11201 02211 11112 20212 12202 01021 ...

Don Knuth, Ambidextrous Numbers, Preprint, September 2022. See (15.3).

Cf. A355904-A355912.

A355905 Leftmost path in the tree T_0 of all negasemiternary (or NST) fractions whose 2-adic part is zero.

Original entry on oeis.org

0, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2, 1, 2, 1, 1, 1, 2, 0, 1, 1, 1, 0, 2, 1, 2, 0, 1, 1

Offset: 0

N. J. A. Sloane, Sep 18 2022

nonn

These are the edge labels in the tree. The initial a(0) = 0 is by convention.

Don Knuth, Ambidextrous Numbers, Preprint, September 2022. See (7.2).

Cf. A355904, A355906-A355913.

A355906 a(0) = 0; for n >= 1, a(n) = -(3/2)*(a(n-1)+A355905(n-1)).

Original entry on oeis.org

0, 0, -3, 3, -6, 9, -15, 21, -33, 48, -75, 111, -168, 252, -381, 570, -858, 1287, -1932, 2898, -4350, 6525, -9789, 14682, -22026, 33039, -49560, 74340, -111513, 167268, -250905, 376356, -564537, 846804, -1270209, 1905312, -2857971, 4286955, -6430434, 9645651

Offset: 0

N. J. A. Sloane, Sep 18 2022

sign

When n is odd, a(n) is the largest multiple of 3 whose NST representation has n digits. When n is even, a(n) is the smallest multiple of 3 with that property.

Don Knuth, Ambidextrous Numbers, Preprint, September 2022. See b_n, (7.3).

Cf. A355904, A355905, A355907-A355913.

More terms from Jinyuan Wang, Sep 29 2022

A355907 A355906(n)/3.

Original entry on oeis.org

0, 0, -1, 1, -2, 3, -5, 7, -11, 16, -25, 37, -56, 84, -127, 190, -286, 429, -644, 966

Offset: 0

N. J. A. Sloane, Sep 18 2022

This is also -(A355905(n)+A355906(n))/2.

Don Knuth, Ambidextrous Numbers, Preprint, September 2022.

Cf. A355904-A355906, A355908-A355913.

A355908 A335905(n) + A335906(n).

Original entry on oeis.org

0, 2, -2, 4, -6, 10, -14, 22, -32, 50, -74, 112, -168, 254, -380, 572, -858, 1288, -1932, 2900

Offset: 0

N. J. A. Sloane, Sep 19 2022

This is also -2*A355907(n).

Don Knuth, Ambidextrous Numbers, Preprint, September 2022.

Cf. A355904-A355907, A355909-A355913.

A355909 Number of nodes at level n in the tree T_0 mentioned in A355905.

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 13, 19, 28, 42, 63, 94, 141, 212, 318, 477, 716, 1074, 1611, 2417, 3626, 5439, 8158, 12237

Offset: 0

N. J. A. Sloane, Sep 19 2022

First differences give A355910.

Don Knuth, Ambidextrous Numbers, Preprint, September 2022. See (8.1), w_n.

Cf. A355904-A355908, A355910-A355913.

a(n) = 1 + (c(n)+c(n-1))/2 where c(n) = |A355908(n)|.

A355910 Number of nodes at level n in the tree T_{-2}.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 6, 9, 14, 21, 31, 47, 71, 106, 159, 239, 358, 537, 806, 1209, 1813, 2719, 4079, 6119

Offset: 0

N. J. A. Sloane, Sep 19 2022

First differences of A355909.

Don Knuth, Ambidextrous Numbers, Preprint, September 2022. See (12.6).

Cf. A355904-A355909, A355911-A355913.

A355911 Number of alt-unary-binary trees with n nodes.

Original entry on oeis.org

1, 1, 2, 2, 2, 4, 4, 4, 4, 6, 8, 8, 8, 8, 8, 12, 12, 14, 16, 16, 16, 16, 16, 16, 24, 24, 24, 26, 28, 28, 32, 32, 32, 32, 32, 32, 32, 40

Offset: 1

N. J. A. Sloane, Sep 19 2022

Don Knuth, Ambidextrous Numbers, Preprint, September 2022. See (13.4).

Cf. A355904-A355910, A355912, A355913.

A355912 Negasemiternary (or NST) representation of the unit ambinumber (0,1).

Original entry on oeis.org

1, 2, 1, 1, 2, 2, 0, 0, 1, 1, 2, 1, 2, 1, 2, 0, 1, 0, 0, 2, 0, 2, 0, 1, 2, 1, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 1, 2, 2, 1, 2, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 1, 2, 2, 2, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1

Offset: 1

N. J. A. Sloane, Sep 19 2022

nonn

			(0, 1) = 1.21122 00112 12120 10020 20121 22002 ...

Don Knuth, Ambidextrous Numbers, Preprint, September 2022. See (15.2).

Cf. A355904-A355911, A355913.

cp's OEIS Frontend

A355913 Negasemiternary (or NST) representation of the unit ambinumber (1,0).

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A355905 Leftmost path in the tree T_0 of all negasemiternary (or NST) fractions whose 2-adic part is zero.

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A355906 a(0) = 0; for n >= 1, a(n) = -(3/2)*(a(n-1)+A355905(n-1)).

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Extensions

A355907 A355906(n)/3.

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A355908 A335905(n) + A335906(n).

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A355909 Number of nodes at level n in the tree T_0 mentioned in A355905.

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Formula

A355910 Number of nodes at level n in the tree T_{-2}.

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A355911 Number of alt-unary-binary trees with n nodes.

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A355912 Negasemiternary (or NST) representation of the unit ambinumber (0,1).

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