1,3

Spiral begins:

49 26--27--28--29--30--31

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48 25 10--11--12--13 32

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47 24 9 2---3 14 33

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46 23 8 1 4 15 34

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45 22 7---6---5 16 35

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44 21--20--19--18--17 36

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43--42--41--40--39--38--37

Michael De Vlieger, Table of n, a(n) for n = 1..10201

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

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 *)

(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

(Python)

from math import isqrt

def A214526(n): return abs((m:=abs(((k:=sum(divmod(s:=isqrt(n-1), 2)))**2<<2)-n+1))-(3*k if m>s else k))+k # Chai Wah Wu, Feb 11 2026 after Kevin Ryde's PARI code

Cf. A137928, A137930, A137931, A002061, A114254, A214176, A214177.

Sequence in context: A386883 A123738 A194511 * A245038 A161312 A161246

Adjacent sequences: A214523 A214524 A214525 * A214527 A214528 A214529

nonn,easy

Alex Ratushnyak, Aug 08 2012

approved