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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 * A346429 A258412 A151927 Adjacent sequences:  A090927 A090928 A090929 * A090931 A090932 A090933 KEYWORD easy,nonn AUTHOR Felix Tubiana, Feb 26 2004 EXTENSIONS Offset corrected by Eric M. Schmidt, May 18 2016 STATUS approved

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Last modified August 15 20:16 EDT 2022. Contains 356148 sequences. (Running on oeis4.)