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A090928 Permutation of natural numbers arising from a square spiral. 6
1, 6, 7, 8, 9, 2, 3, 4, 5, 18, 19, 20, 21, 22, 23, 24, 25, 10, 11, 12, 13, 14, 15, 16, 17, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 50, 51, 52, 53, 54, 55, 56 (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 counterclockwise spiral: 1 -> 6 -> 7 -> 8 -> 9 -> 2 -> 3 -> 4 -> 5 -> 18 -> 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[If[n +4*x <= (2*x+1)^2, n+4*x, n-4*x], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)

PROG

(Sage)

def a(n):

    x = (isqrt(n-1)+1)//2

    return n + 4*x if n + 4*x <= (2*x+1)^2 else n - 4*x

[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(if(n+4*s(n) <= (2*s(n)+1)^2, n +4*s(n), n - 4*s(n)), ", ")) \\ G. C. Greubel, Feb 05 2019

CROSSREFS

Cf. A020703, A090861, A090915, A090925, A090929, A090930.

Sequence in context: A202703 A308147 A308165 * A199174 A335094 A153604

Adjacent sequences:  A090925 A090926 A090927 * A090929 A090930 A090931

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 November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)