|
| |
|
|
A244677
|
|
The spiral of Champernowne, read along the East ray.
|
|
24
|
|
|
|
1, 2, 0, 1, 1, 4, 8, 9, 1, 1, 6, 8, 2, 4, 8, 3, 6, 0, 4, 9, 5, 6, 6, 1, 7, 4, 1, 9, 0, 1, 1, 1, 7, 1, 4, 7, 6, 1, 6, 6, 7, 1, 0, 9, 0, 2, 3, 5, 5, 2, 7, 4, 2, 3, 1, 6, 1, 3, 5, 1, 2, 3, 0, 9, 5, 4, 5, 1, 0, 4, 1, 6, 7, 5, 6, 4, 6, 6, 3, 5, 7, 6, 9, 0, 0, 7, 6, 8, 5, 8, 3, 9, 2, 8, 0, 3, 1, 9, 8, 0, 0, 3, 0, 4, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Inspired by Stanislaw Ulam's spiral, circa 1963.
|
|
|
LINKS
|
|
|
|
FORMULA
|
Formulas for rays in directions of 32 compass points:
SE 4n^2 -4n +1
SExS 64n^2 -113n +50
SSE 16n^2 -25n +10
SxE 64n^2 -115n +52
S 4n^2 -5n +2
SxW 64n^2 -117n +54
SSW 16n^2 -27n +12
SWxS 64n^2 -119n +56
SW 4n^2 -6n +3
SWxW 64n^2 -121n +58
WSW 16n^2 -29n +14
WxS 64n^2 -123n +60
W 4n^2 -7n +4
WxN 64n^2 -125n +62
WNW 16n^2 -31n +16
NWxW 64n^2 -127n +64
NW 4n^2 -8n +5
NWxN 64n^2 -129n +66
NNW 16n^2 -33n +18
NxW 64n^2 -131n +68
N 4n^2 -9n +6
NxE 64n^2 -133n +70
NNE 16n^2 -35n +20
NExN 64n^2 -135n +72
NE 4n^2 -10n +7
NExE 64n^2 -137n +74
ENE 16n^2 -37n +22
ExN 64n^2 -139n +76
E 4n^2 -11n +8
ExS 64n^2 -141n +78
ESE 16n^2 -39n +24
SExE 64n^2 -143n +80
|
|
|
EXAMPLE
|
The beginning of the infinite spiral of David Gawen Champernowne:
.
7--1--9--6--1--8--6--1--7--6--1--6--6--1--5--6--1--4--6--1--3 .
| | |
0 1--4--4--1--3--4--1--2--4--1--1--4--1--0--4--1--9--3--1 6 .
| | | | |
1 4 2--1--1--2--1--0--2--1--9--1--1--8--1--1--7--1--1 8 1 .
| | | | | | |
7 5 2 0--1--1--0--1--0--0--1--9--9--8--9--7--9--6 6 3 2 9
| | | | | | | | |
1 1 1 2 7--7--6--7--5--7--4--7--3--7--2--7--1 9 1 1 6 8
| | | | | | | | | | |
1 4 2 1 7 5--5--4--5--3--5--2--5--1--5--0 7 5 1 7 1 1
| | | | | | | | | | | | |
7 6 3 0 8 5 7--3--6--3--5--3--4--3--3 5 0 9 5 3 1 8
| | | | | | | | | | | | | | |
2 1 1 3 7 6 3 3--2--2--2--1--2--0 3 9 7 4 1 1 6 8
| | | | | | | | | | | | | | | | |
1 4 2 1 9 5 8 2 3--1--2--1--1 2 2 4 9 9 1 6 1 1
| | | | | | | | | | | | | | | | | | |
7 7 4 0 8 7 3 4 1 5--4--3 1 9 3 8 6 3 4 3 0 7
| | | | | | | | | | | | | | | | | | | | |
3 1 1 4 0 5 9 2 4 6 1--2 0 1 1 4 8 9 1 1 6 8
| | | | | | | | | | | | | | | | | | | |
1 4 2 1 8 8 4 5 1 7--8--9--1 8 3 7 6 2 1 5 1 1
| | | | | | | | | | | | | | | | | |
7 8 5 0 1 5 0 2 5--1--6--1--7--1 0 4 7 9 3 3 9 6
| | | | | | | | | | | | | | | |
4 1 1 5 8 9 4 6--2--7--2--8--2--9--3 6 6 1 1 1 5 8
| | | | | | | | | | | | | |
1 4 2 1 2 6 1--4--2--4--3--4--4--4--5--4 6 9 1 4 1 1
| | | | | | | | | | | |
7 9 6 0 8 0--6--1--6--2--6--3--6--4--6--5--6 0 2 3 8 5
| | | | | | | | | |
5 1 1 6 3--8--4--8--5--8--6--8--7--8--8--8--9--9 1 1 5 8
| | | | | | | |
1 5 2 1--0--7--1--0--8--1--0--9--1--1--0--1--1--1--1 3 1 1
| | | | | |
7 0 7--1--2--8--1--2--9--1--3--0--1--3--1--1--3--2--1--3 7 4
| | | |
6 1--5--1--1--5--2--1--5--3--1--5--4--1--5--5--1--5--6--1--5 8
| |
1--7--7--1--7--8--1--7--9--1--8--0--1--8--1--1--8--2--1--8--3--1
|
|
|
MATHEMATICA
|
almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_] := 4n^2 - 11n + 8 (* see formula section *); Array[ almostNatural[ f@#, 10] &, 105]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
