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A211000 Coordinates (x,y) of the endpoint of a structure (or curve) formed by Q-toothpicks in which the inflection points are the prime numbers A000040. 12
0, 0, 1, 1, 2, 0, 3, -1, 4, -2, 3, -3, 2, -4, 3, -5, 4, -6, 3, -7, 2, -6, 3, -5, 4, -4, 3, -3, 2, -2, 3, -1, 4, -2, 3, -3, 2, -4, 3, -5, 4, -6, 3, -7, 2, -6, 3, -5, 4, -4, 3, -3, 2, -4, 3, -5, 4, -4, 3, -3, 2, -2, 3, -1, 4, 0, 3, 1, 2, 0, 3, -1, 4, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

On the infinite square grid the structure looks like a column of tangent circles of radius 1. The structure arises from the prime numbers A000040. The behavior seems to be as modular arithmetic but in a growing structure. The values ​​on the axis "x" are easy to predict (see A211010). On the other hand the values ​​on the axis "y" do not seem to be predictable (see A211011). This is a member of the family of the structures or curves mentioned in A210838. The odd numbers > 1 are located on the main axis of the structure. Note that here the Q-toothpicks can be superposed. For the definition of Q-toothpicks see A187210. A211021 gives the number of stage where a new circle appears in the structure. For the number of circles after n-th stage see A211020.  For the location of the centers of the circles see A211022. For the sums of the visible nodes after n-th stage see A211024.

LINKS

Table of n, a(n) for n=0..73.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to toothpick sequences

EXAMPLE

We start at stage 0 with no Q-toothpicks.

At stage 1 we place a Q-toothpick centered at (1,0) with its endpoints at (0,0) and (1,1).

At stage 2 we place a Q-toothpick centered at (1,0) with its endpoints at (1,1) and (2,0). Since 2 is a prime number we have that the end of the curve is also an inflection point.

At stage 3 we place a Q-toothpick centered at (3,0) with its endpoints at (2,0) and (3,-1). Since 3 is a prime number we have that the end of the curve is also an inflection point.

At stage 4 we place a Q-toothpick centered at (3,-2) with its endpoints at (3,-1) and (4,-2).

-------------------------------------

.                    The end as

.          Pair      inflection

n        (x    y)      point

-------------------------------

0         0,   0,        -

1         1,   1,        -

2         2,   0,       Yes

3         3,  -1,       Yes

4         4,  -2,        -

5         3,  -3,       Yes

6         2,  -4,        -

7         3,  -5,       Yes

8         4,  -6,        -

9         3,  -7,        -

10        2,  -6,        -

11        3,  -5,       Yes

...

Illustration of the nodes of the structure:

-----------------------------------------------------

After 9 stages    After 10 stages    After 11 stages

-----------------------------------------------------

.

.    1                 1                  1

.  0   2             0   2              0   2

.        3                 3                  3

.          4                 4                  4

.        5                 5                  5

.      6                 6                  6

.        7                 7                 11

.          8            10   8             10   8

.        9                 9                  9

.

CROSSREFS

Bisections: A211010, A211011.

Cf. A187210, A210838, A210841, A211001-A211003, A211020-A211024.

Sequence in context: A215589 A274185 A161162 * A025636 A025637 A195826

Adjacent sequences:  A210997 A210998 A210999 * A211001 A211002 A211003

KEYWORD

sign

AUTHOR

Omar E. Pol, Mar 30 2012

STATUS

approved

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Last modified August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)