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 A090929 Permutation of natural numbers arising from a square spiral. 6
 1, 8, 9, 2, 3, 4, 5, 6, 7, 22, 23, 24, 25, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 44, 45, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 74, 75, 76, 77, 78, 79, 80, 81, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 (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 -> 8 -> 9 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 22 -> 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 +6*x <= (2*x+1)^2, n +6*x, n -2*x], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *) PROG (Sage) def a(n):     x = (isqrt(n-1)+1)//2     return n + 6*x if n + 6*x <= (2*x+1)^2 else n - 2*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+6*s(n) <= (2*s(n)+1)^2, n +6*s(n), n - 2*s(n)), ", ")) \\ G. C. Greubel, Feb 05 2019 CROSSREFS Cf. A020703, A090861, A090915, A090925, A090928, A090930. Sequence in context: A334751 A289252 A064734 * A113210 A021116 A201406 Adjacent sequences:  A090926 A090927 A090928 * A090930 A090931 A090932 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 27 07:28 EST 2021. Contains 349365 sequences. (Running on oeis4.)