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.

Previous Showing 11-16 of 16 results.

A171166 A polyspiral path: a(n) represents the n-th vertex of a lattice path with an infinite number of finite square spirals.

Original entry on oeis.org

0, 2, 4, 5, 6, 11, 16, 19, 22, 24, 26, 27, 28, 36, 44, 49, 54, 58, 62, 65, 68, 70, 72, 73, 74, 85, 96, 103, 110, 116, 122, 127, 132, 136, 140, 143, 146, 148, 150, 151, 152, 166, 180, 189, 198, 206, 214, 221, 228, 234, 240, 245, 250, 254, 258
Offset: 0

Views

Author

Omar E. Pol, Mar 14 2010

Keywords

Comments

Also, partial sums of the sequence formed by 0 together with the numbers of A171176 repeated.
For another version see A171165.

Crossrefs

Extensions

Edited by Omar E. Pol, Mar 16 2010

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;
...
		

Crossrefs

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;
...
		

Crossrefs

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).

Crossrefs

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).

Crossrefs

A210610 Number of semicircumferences in the n-th spiral of the structure mentioned in A210606.

Original entry on oeis.org

3, 11, 4, 10, 4, 28, 10, 24, 8, 2, 4, 9, 4, 2, 36, 12, 4, 2, 3, 28, 10, 52, 18, 32, 12, 15, 38, 14, 32, 12, 44, 16, 148, 50, 7, 22, 8, 3, 4, 2, 70, 24, 114, 42, 200, 68, 6, 2, 13
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.

Crossrefs

Previous Showing 11-16 of 16 results.