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 A214526 Manhattan distances between n and 1 in a square spiral with positive integers and 1 at the center. 24
 0, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Spiral begins:   49  26--27--28--29--30--31    |   |                   |   48  25  10--11--12--13  32    |   |   |           |   |   47  24   9   2---3  14  33    |   |   |   |   |   |   |   46  23   8   1   4  15  34    |   |   |       |   |   |   45  22   7---6---5  16  35    |   |               |   |   44  21--20--19--18--17  36    |                       |   43--42--41--40--39--38--37 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10201 FORMULA abs( a(n) - a(n-1) ) = 1. For n > 1, a(n) = layer(n) + abs(((n-1) mod (2*layer(n)) - layer(n))) (conjectured) where layer(n) = ceiling(0.5*sqrt(n) - 0.5). - Karl R. Stephan, Jan 26 2018 a(n) = abs(A174344(n)) + abs(A274923(n)). - Kevin Ryde, Oct 25 2019 MATHEMATICA f[n_] := Block[{o = 2 n - 1, t, w}, t = Table[0, {o}, {o}]; t = ReplacePart[t, {n, n} -> 1]; Do[w = Partition[Range[(2 (# - 1) - 1)^2 + 1, (2 # - 1)^2], 2 (# - 1)] &@ k; Do[t = ReplacePart[t, {(n + k) - (j + 1), n + (k - 1)} -> #[[1, j]]]; t = ReplacePart[t, {n - (k - 1), (n + k) - (j + 1)} -> #[[2, j]]]; t = ReplacePart[t, {(n - k) + (j + 1), n - (k - 1)} -> #[[3, j]]]; t = ReplacePart[t, {n + (k - 1), (n - k) + (j + 1)} -> #[[4, j]]], {j, 2 (k - 1)}] &@ w, {k, 2, n}]; t]; With[{x = Position[#, 1][[1]]}, Table[Total@ Abs[Position[#, n][[1]] - x], {n, Max@ #}]] &@ f@ 6 (* Michael De Vlieger, Feb 16 2018 *) PROG (PARI) a(n) = n--; my(m=sqrtint(n), k=ceil(m/2)); n=abs(n-4*k^2); k+abs(n-if(n>m, 3, 1)*k); \\ Kevin Ryde, Oct 25 2019 CROSSREFS Cf. A137928, A137930, A137931, A002061, A114254, A214176, A214177. Sequence in context: A175835 A123738 A194511 * A245038 A161312 A161246 Adjacent sequences:  A214523 A214524 A214525 * A214527 A214528 A214529 KEYWORD nonn,easy AUTHOR Alex Ratushnyak, Aug 08 2012 STATUS approved

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Last modified May 26 13:17 EDT 2022. Contains 354092 sequences. (Running on oeis4.)