OFFSET
1,2
COMMENTS
Inspired by Stanislaw Ulam's spiral, circa 1963.
LINKS
Robert G. Wilson v, Cover of the March 1964 issue of Scientific American
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 .
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0 1--4--4--1--3--4--1--2--4--1--1--4--1--0--4--1--9--3--1 6 .
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1 4 2--1--1--2--1--0--2--1--9--1--1--8--1--1--7--1--1 8 1 .
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7 5 2 0--1--1--0--1--0--0--1--9--9--8--9--7--9--6 6 3 2 9
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1 1 1 2 7--7--6--7--5--7--4--7--3--7--2--7--1 9 1 1 6 8
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1 4 2 1 7 5--5--4--5--3--5--2--5--1--5--0 7 5 1 7 1 1
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7 6 3 0 8 5 7--3--6--3--5--3--4--3--3 5 0 9 5 3 1 8
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2 1 1 3 7 6 3 3--2--2--2--1--2--0 3 9 7 4 1 1 6 8
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1 4 2 1 9 5 8 2 3--1--2--1--1 2 2 4 9 9 1 6 1 1
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7 7 4 0 8 7 3 4 1 5--4--3 1 9 3 8 6 3 4 3 0 7
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3 1 1 4 0 5 9 2 4 6 1--2 0 1 1 4 8 9 1 1 6 8
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1 4 2 1 8 8 4 5 1 7--8--9--1 8 3 7 6 2 1 5 1 1
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7 8 5 0 1 5 0 2 5--1--6--1--7--1 0 4 7 9 3 3 9 6
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4 1 1 5 8 9 4 6--2--7--2--8--2--9--3 6 6 1 1 1 5 8
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1 4 2 1 2 6 1--4--2--4--3--4--4--4--5--4 6 9 1 4 1 1
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7 9 6 0 8 0--6--1--6--2--6--3--6--4--6--5--6 0 2 3 8 5
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5 1 1 6 3--8--4--8--5--8--6--8--7--8--8--8--9--9 1 1 5 8
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1 5 2 1--0--7--1--0--8--1--0--9--1--1--0--1--1--1--1 3 1 1
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7 0 7--1--2--8--1--2--9--1--3--0--1--3--1--1--3--2--1--3 7 4
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6 1--5--1--1--5--2--1--5--3--1--5--4--1--5--5--1--5--6--1--5 8
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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
Robert G. Wilson v, Jul 04 2014
STATUS
approved