A275609 -id:A275609 - cp's OEIS frontend

A307193 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the East spoke starting at the origin.

0, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3

Offset: 0

N. J. A. Sloane, Mar 29 2019

nonn

The Example section of A275609 shows the central portion of the spiral very clearly. The link below shows a larger portion but is harder to read.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Central portion of spiral, shown without spaces [The central 0 (at (0,0)) has been changed to an X. The illustration shows cells (x,y) with -35 <= x <= 35, -33 <= y <= 36.] The present sequence gives the numbers to the East of the X.

Cf. A275609.

The eight spokes starting at the origin are A307193 - A307200.

More terms from Alois P. Heinz, Mar 30 2019

A307200 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the South-East spoke starting at the origin.

Original entry on oeis.org

0, 2, 3, 2, 3, 2, 3, 2, 1, 0, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 1, 0, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 1, 0, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 1, 0, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3

Offset: 0

N. J. A. Sloane, Mar 29 2019

nonn

The Example section of A275609 shows the central portion of the spiral very clearly. The link below shows a larger portion but is harder to read.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Central portion of spiral, shown without spaces [The central 0 (at (0,0)) has been changed to an X. The illustration shows cells (x,y) with -35 <= x <= 35, -33 <= y <= 36.] The present sequence gives the numbers to the South-East of the X.

Cf. A275609.

The eight spokes starting at the origin are A307193 - A307200.

More terms from Alois P. Heinz, Mar 30 2019

A307188 Positions of 0's in the square spiral in A275609.

Original entry on oeis.org

0, 9, 11, 14, 16, 18, 20, 22, 30, 47, 49, 51, 53, 59, 61, 63, 66, 68, 70, 72, 74, 76, 88, 90, 92, 100, 117, 119, 121, 123, 125, 127, 137, 139, 141, 147, 149, 151, 153, 155, 158, 160, 162, 178, 180, 182, 184, 186, 194, 196, 198, 210, 219, 221, 223, 225, 227

Offset: 1

N. J. A. Sloane, Mar 28 2019

nonn

This sequence and A307189-A307192 together partition the nonnegative numbers.
Comment from N. J. A. Sloane, Mar 31 2019: (Start)
Both Rémy Sigrist's illustration and mine show the same block structure. A block B(r,s) will mean an array of r X s 0's separated by rows and columns of blanks. Here is B(3,5), with blanks represented by dots:
......
0.0.0.
......
0.0.0.
......
0.0.0.
The dots are always to the right of or above the 0's.
The block B(r,s) has size 2r X 2s.
The block containing the center point is a B(3,5).
Looking at the blocks along the x-axis, moving from West to East, the successive r-values are:
... 23, 19, 15, 11, 7, (3), 5, 9, 13, 17, 21, ...
Looking at the blocks along the y-axis, moving from South to North, the successive s-values are:
... 24, 20, 16, 12, 8, (5), 6, 10, 14, 18, 22, ...
Except at the central block B(3,5), the differences between adjacent r- and s-values always have magnitude 4.
Furthermore, as we move North, each block is displaced by one step to the East from the block below it. As we move East, each block is displaced by one step to the South from the block to the West of it.
These displacements can be seen in both illustrations. In Sigrist's illustration, notice how the blocks gradually shift to the East along the y-xis, and to the South along along the x-axis.
(End)

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1240 terms from N. J. A. Sloane)
Rémy Sigrist, Colored scatterplot of (x,y) such that A275609(x,y) = 0 and -500 <= x <= 500 and -500 <= y <= 500 (where the color is function of (x mod 2) + 2 * (y mod 2))
N. J. A. Sloane, Central portion of spiral in A275609 showing just the 0's [Entries 1,2,3,4 in the spiral have been replaced by dots. The central 0 has been changed to an X. The illustration shows cells (x,y) with -35 <= x <= 35, -33 <= y <= 36.]

Cf. A275609, A307189-A307192.

A307192 Positions of 4's in the square spiral in A275609.

Original entry on oeis.org

13, 37, 62, 102, 140, 157, 200, 217, 250, 290, 330, 359, 392, 443, 452, 492, 525, 566, 629, 651, 686, 723, 768, 772, 847, 889, 912, 953, 1009, 1097, 1157, 1170, 1215, 1279, 1379, 1459, 1468, 1509, 1581, 1693, 1781, 1807, 1835, 1915, 1996, 2039, 2135

Offset: 1

N. J. A. Sloane, Mar 28 2019

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..2886
Rémy Sigrist, Colored scatterplot of (x,y) such that A275609(x,y) = 4 and -500 <= x <= 500 and -500 <= y <= 500 (where the color is function of (x mod 2) + 2 * (y mod 2))
N. J. A. Sloane, Central portion of spiral in A275609 showing just the 4's [Entries 0,1,2,3 in the spiral have been replaced by dots. The central 0 has been changed to an X. The illustration shows cells (x,y) with -35 <= x <= 35, -33 <= y <= 36.]

Cf. A275609, A307188-A307191.

A307191 Positions of 3's in the square spiral in A275609.

Original entry on oeis.org

3, 7, 10, 17, 19, 24, 29, 32, 34, 43, 45, 50, 52, 57, 65, 67, 69, 71, 78, 80, 87, 89, 94, 96, 99, 111, 113, 115, 122, 124, 126, 133, 135, 145, 148, 150, 152, 154, 164, 166, 168, 177, 179, 181, 188, 190, 193, 195, 209, 212, 214, 216, 226, 228, 230, 232, 241

Offset: 1

N. J. A. Sloane, Mar 28 2019

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1216 terms from N. J. A. Sloane)
Rémy Sigrist, Colored scatterplot of (x,y) such that A275609(x,y) = 3 and -500 <= x <= 500 and -500 <= y <= 500 (where the color is function of (x mod 2) + 2 * (y mod 2))

Cf. A275609, A307188-A307192.

A307189 Positions of 1's in the square spiral in A275609.

Original entry on oeis.org

1, 4, 6, 12, 23, 25, 27, 33, 35, 38, 40, 42, 44, 54, 56, 58, 64, 77, 79, 81, 83, 85, 95, 97, 103, 105, 107, 109, 112, 114, 128, 130, 132, 134, 136, 142, 144, 146, 156, 163, 165, 167, 169, 171, 173, 175, 189, 191, 201, 203, 205, 207, 213, 215, 234, 236, 238

Offset: 1

N. J. A. Sloane, Mar 28 2019

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1249 terms from N. J. A. Sloane)
Rémy Sigrist, Colored scatterplot of (x,y) such that A275609(x,y) = 1 and -500 <= x <= 500 and -500 <= y <= 500 (where the color is function of (x mod 2) + 2 * (y mod 2))

Cf. A275609, A307188, A307190, A307191, A307192.

A307190 Positions of 2's in the square spiral in A275609.

Original entry on oeis.org

2, 5, 8, 15, 21, 26, 28, 31, 36, 39, 41, 46, 48, 55, 60, 73, 75, 82, 84, 86, 91, 93, 98, 101, 104, 106, 108, 110, 116, 118, 120, 129, 131, 138, 143, 159, 161, 170, 172, 174, 176, 183, 185, 187, 192, 197, 199, 202, 204, 206, 208, 211, 218, 220, 222, 224, 235

Offset: 1

N. J. A. Sloane, Mar 28 2019

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1216 terms from N. J. A. Sloane)
Rémy Sigrist, Colored scatterplot of (x,y) such that A275609(x,y) = 2 and -500 <= x <= 500 and -500 <= y <= 500 (where the color is function of (x mod 2) + 2 * (y mod 2))

Cf. A275609, A307188-A307192.

A307194 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the North-East spoke starting at the origin.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Mar 29 2019

nonn

The Example section of A275609 shows the central portion of the spiral very clearly. The link below shows a larger portion but is harder to read.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Central portion of spiral, shown without spaces [The central 0 (at (0,0)) has been changed to an X. The illustration shows cells (x,y) with -35 <= x <= 35, -33 <= y <= 36.] The present sequence gives the numbers to the North-East of the X.

Cf. A275609.

The eight spokes starting at the origin are A307193 - A307200.

More term from Alois P. Heinz, Mar 30 2019

A307195 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the North spoke starting at the origin.

Original entry on oeis.org

0, 3, 0, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 3, 1, 3, 1, 3, 1, 3

Offset: 0

N. J. A. Sloane, Mar 29 2019

nonn

The Example section of A275609 shows the central portion of the spiral very clearly. The link below shows a larger portion but is harder to read.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Central portion of spiral, shown without spaces [The central 0 (at (0,0)) has been changed to an X. The illustration shows cells (x,y) with -35 <= x <= 35, -33 <= y <= 36.] The present sequence gives the numbers to the North of the X.

Cf. A275609.

The eight spokes starting at the origin are A307193 - A307200.

More terms from Alois P. Heinz, Mar 30 2019

A307196 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the North-West spoke starting at the origin.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Mar 29 2019

nonn

The Example section of A275609 shows the central portion of the spiral very clearly. The link below shows a larger portion but is harder to read.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Central portion of spiral, shown without spaces [The central 0 (at (0,0)) has been changed to an X. The illustration shows cells (x,y) with -35 <= x <= 35, -33 <= y <= 36.] The present sequence gives the numbers to the North-West of the X.

Cf. A275609.

The eight spokes starting at the origin are A307193 - A307200.

More terms from Alois P. Heinz, Mar 30 2019

cp's OEIS Frontend

A307193 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the East spoke starting at the origin.

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A307200 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the South-East spoke starting at the origin.

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A307188 Positions of 0's in the square spiral in A275609.

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A307192 Positions of 4's in the square spiral in A275609.

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A307191 Positions of 3's in the square spiral in A275609.

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A307189 Positions of 1's in the square spiral in A275609.

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A307190 Positions of 2's in the square spiral in A275609.

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Crossrefs

A307194 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the North-East spoke starting at the origin.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A307195 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the North spoke starting at the origin.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A307196 Fill the plane with the square spiral with cells numbered as in A275609; sequence gives the cells along the North-West spoke starting at the origin.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions