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A090915
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Permutation of natural numbers arising from a square spiral.
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6
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1, 8, 7, 6, 5, 4, 3, 2, 9, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 25, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 49, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58
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OFFSET
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1,2
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COMMENTS
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Write out the natural numbers in a square counterclockwise spiral:
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17--16--15--14--13
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18 5---4---3 12
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19 6 1---2 11
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20 7---8---9--10
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21--22--23--24--25
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Now read off the numbers in a square clockwise spiral: 1 -> 8 -> 7 -> 6 -> 5 -> 4 -> 3 -> 2 -> 9 -> etc.
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LINKS
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MATHEMATICA
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With[{x = Floor[(Floor[Sqrt[n-1]]+1)/2]}, Table[If[n==(2*x+1)^2, n, 8*x^2 -n+2], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)
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PROG
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(Sage)
def a(n):
x = (isqrt(n-1)+1)//2
return n if n == (2*x+1)^2 else 8*x^2 + 2 - n
(PARI) {s(n) = ((sqrtint(n-1)+1)/2)\1};
for(n=1, 75, print1(if(n == (2*s(n)+1)^2, n, 8*s(n)^2-n+2), ", ")) \\ G. C. Greubel, Feb 05 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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