cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A210606 Length of the n-th edge of an L-toothpick structure which gives Recamán's sequence A005132.

Original entry on oeis.org

1, 3, 5, 3, 4, 4, 5, 11, 13, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17
Offset: 1

Views

Author

Omar E. Pol, Mar 24 2012

Keywords

Comments

Consider a toothpick structure formed by L-toothpicks connected by their endpoints. The endpoints of the L-toothpicks are placed on the main diagonal of the first quadrant. At stage 1 we place an L-toothpick with one of its endpoints on the origin. At stage n we place an L-toothpick of size n. The L-toothpicks are placed alternately, on one or another sector of the first quadrant, trying to make the structure have an exposed endpoint closest to the origin. The total length of all L-toothpicks after the n-th stage is A002378(n). The value of x and y of the endpoint of the structure after the n-th stage is equal to the n-th term of Recamán's sequence A005132(n). Note that we can get other illustrations of initial terms of Recamán's sequence by replacing each L-toothpick by a Q-toothpick or by a semicircumference. This structure is also one of the three views of the three-dimensional model for Recamán's sequence. For more information about L-toothpicks and Q-toothpicks, see A172310 and A187210.

Examples

			The summands are the size of the L-toothpicks:
a(1) = 1.
a(2) = 1 + 2 = 3.
a(3) = 2 + 3 = 5.
a(4) = 3.
a(5) = 4.
a(6) = 4.
a(7) = 5.
a(8) = 5 + 6 = 11.
a(9) = 6 + 7 = 13.
a(10) = 7.

Links

Crossrefs

First differences of A210607.
Cf. A005132, A064289, A119632, A139250, A160356, A160357, A171175, A171178, A172310, A187210, A210604, A210605, A210608-A210613.

A210604 Bisection of Recamán's sequence A005132.

Original entry on oeis.org

0, 3, 2, 13, 12, 11, 10, 9, 8, 43, 42, 41, 42, 43, 44, 45, 46, 113, 114, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 157, 156, 155, 154, 153, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 367, 368, 369, 370, 151, 152
Offset: 1

Views

Author

Omar E. Pol, Mar 23 2012

Keywords

Comments

Also length of the horizontal edges of a rectangular polyspiral path. For the vertical edges see A210605. The mentioned polyspiral path is one of the three views of a rectangular polyhelix which is a three-dimensional graphical representation of Recamán's sequence A005132.

Examples

			1) Written as an irregular array in which each row lists consecutive numbers in ascending order or in descending order:
0;
3,2;
13,12,11,10,9,8;
43,42,41;
42,43,44,45,46;
113,114;
39,38,37,36,35,34,33,32,31,30,29,28,27,26;
...
2) Written as an irregular array in which each row lists consecutive numbers in ascending order, in descending order or in descending-ascending order:
0;
3,2;
13,12,11,10,9,8;
43,42,41,42,43,44,45,46;
113,114;
39,38,37,36,35,34,33,32,31,30,29,28,27,26;
...

Links

Crossrefs

Cf. A005132, A065056, A171175, A171178, A210605-A210607.

A210605 Bisection of Recamán's sequence A005132.

Original entry on oeis.org

1, 6, 7, 20, 21, 22, 23, 24, 25, 62, 63, 18, 17, 16, 15, 14, 79, 78, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 224, 225, 226, 227, 228, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 265, 264, 263, 262, 261, 40, 265, 494, 495, 258, 259
Offset: 1

Views

Author

Omar E. Pol, Mar 23 2012

Keywords

Comments

Also length of the vertical edges of a rectangular polyspiral path. For the horizontal edges see A210604. The mentioned polyspiral path is one of the three views of a rectangular polyhelix which is a three-dimensional graphical representation of Recamán's sequence A005132.

Examples

			1) Written as an irregular array in which each row lists consecutive numbers in ascending order or in descending order:
1;
6,7;
20,21,22,23,24,25;
62,63;
18,17,16,15,14;
79,78,77;
78,79,80,81,82,83,84,85,86,87,88,89,90,91;
...
2) Written as an irregular array in which each row lists consecutive numbers in ascending order, in descending order or in descending-ascending order:
1;
6,7;
20,21,22,23,24,25;
62,63;
18,17,16,15,14;
79,78,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91;
...

Links

Crossrefs

Cf. A005132, A065056, A171175, A171178, A210604-A210607.

A210608 Number of intersections after n-th stage in the structure mentioned in A210606 using semicircumferences and counting the superposed intersections several times.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 14, 22, 28, 36, 43
Offset: 1

Views

Author

Omar E. Pol, Mar 25 2012

Keywords

Comments

The structure mentioned in A210606 is a model for the visualization of Recamán's sequence A005132.
First differs from A210609 at a(24).

Links

Crossrefs

Cf. A005132, A064289, A119632, A160356, A160357, A171175, A171178, A210606, A210607, A210609-A210613.

A210609 Number of intersections after n-th stage in the structure mentioned in A210606 using semicircumferences and counting the superposed intersections only once.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 14, 21, 27
Offset: 1

Views

Author

Omar E. Pol, Mar 25 2012

Keywords

Comments

The structure mentioned in A210606 is a model for the visualization of Recamán's sequence A005132.
First differs from A210608 at a(24).

Links

Crossrefs

Cf. A005132, A064289, A119632, A160356, A160357, A171175, A171178, A210606, A210607, A210608, A210610-A210613.
Showing 1-5 of 5 results.

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