A317620 Squares visited by a (2,4)-leaper on a spirally numbered board and moving to the lowest available unvisited square at each step.

1, 51, 13, 19, 25, 15, 21, 11, 17, 23, 53, 59, 129, 135, 61, 55, 125, 79, 161, 71, 77, 159, 153, 67, 141, 147, 69, 63, 137, 131, 233, 123, 165, 75, 157, 267, 73, 151, 65, 139, 57, 127, 81, 163, 277, 155, 265, 407, 145, 251, 389, 243, 237, 371, 229, 167

Offset

1,2

Comments

Board is numbered with the square spiral:

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17--16--15--14--13

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18 5---4---3 12 .

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19 6 1---2 11 .

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20 7---8---9--10 .

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21--22--23--24--25--26

.

The sequence is finite: at step 2016, square 8399 is visited, after which there are no unvisited squares within one move.

Links

Daniël Karssen, Table of n, a(n) for n = 1..2016

Daniël Karssen, Figure showing the first 29 steps of the sequence

Daniël Karssen, Figure showing the complete sequence

Formula

a(n) = A317619(n-1) + 1.

Mathematica

spiral[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]; Block[{nn = 30, j = {2, 4}, k = 1, t}, t = spiral[nn]; (k - 1) + Nest[Function[{a}, Append[a, SelectFirst[Sort@ Map[{t[[##]], ##} & @@ {#1 + a[[-1, 2]], #2 + a[[-1, 3]]} & @@ # &, Join @@ Inner[Times, Tuples[{-1, 1}, {2}], Permutations[j], List]], FreeQ[a[[All, 1]], First[#] ] &]]], {{1, nn, nn}}, 55][[All, 1]] ] (* Michael De Vlieger, Aug 02 2018 *)

Crossrefs

Cf. A317619, A317622.

Sequence in context: A087408 A255852 A160474 * A317415 A033371 A191514

Adjacent sequences: A317617 A317618 A317619 * A317621 A317622 A317623

Keyword

nonn,fini,full

Author

Daniël Karssen, Aug 01 2018

Status

approved