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A090930 Permutation of natural numbers arising from a square spiral. 6
1, 2, 9, 8, 7, 6, 5, 4, 3, 12, 11, 10, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 30, 29, 28, 27, 26, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 56, 55, 54, 53, 52, 51, 50, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Write out the natural numbers in a square counterclockwise spiral:

.

  17--16--15--14--13

   |               |

  18   5---4---3  12

   |   |       |   |

  19   6   1---2  11

   |   |           |

  20   7---8---9--10

   |

  21--22--23--24--25

.

Now read off the numbers in a clockwise spiral: 1 -> 2 -> 9 -> 8 -> 7 -> 6 -> 5 -> 4 -> 3 -> 12 -> etc.

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

MATHEMATICA

With[{x = Floor[(Floor[Sqrt[n-1]] +1)/2]}, Table[8*x^2 -n +2 +x*If[n <= 4*x^2 -2*x, -6, 2], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)

PROG

(Sage)

def a(n):

    x = (isqrt(n-1)+1)//2

    return 8*x^2 + (-6 if n <= 4*x^2 - 2*x else 2)*x + 2 - n

[a(n) for n in (1..75)]

# Eric M. Schmidt, May 18 2016

(PARI) {s(n) = ((sqrtint(n-1)+1)/2)\1};

for(n=1, 75, print1(8*s(n)^2 -n +2 +s(n)*if(n <= 2*s(n)*(2*s(n)-1), -6, 2), ", ")) \\ G. C. Greubel, Feb 05 2019

CROSSREFS

Cf. A020703, A090861, A090915, A090925, A090928, A090929.

Sequence in context: A018799 A076219 A077601 * A258412 A151927 A046017

Adjacent sequences:  A090927 A090928 A090929 * A090931 A090932 A090933

KEYWORD

easy,nonn

AUTHOR

Felix Tubiana (fat2(AT)columbia.edu), Feb 26 2004

EXTENSIONS

Offset corrected by Eric M. Schmidt, May 18 2016

STATUS

approved

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Last modified June 14 10:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)