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A217014 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of triangular horizontal-last spiral (defined in A214226).

%I A217014 #8 Mar 12 2025 20:15:32
%S A217014 1,7,22,8,2,3,4,6,20,42,21,44,75,45,23,9,11,12,13,14,15,5,19,41,71,
%T A217014 109,72,43,74,113,160,114,76,46,24,10,28,29,30,31,32,33,34,16,18,40,
%U A217014 70,108,154,208,155,110,73,112,159,214
%N A217014 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of triangular horizontal-last spiral (defined in A214226).
%o A217014 (Python)
%o A217014 SIZE = 33       # must be 4k+1
%o A217014 grid = [0] * (SIZE*SIZE)
%o A217014 posX = posY = SIZE//2
%o A217014 grid[posY*SIZE+posX]=1
%o A217014 n = 2
%o A217014 def walk(stepX, stepY, chkX, chkY):
%o A217014   global posX, posY, n
%o A217014   while 1:
%o A217014     posX+=stepX
%o A217014     posY+=stepY
%o A217014     grid[posY*SIZE+posX]=n
%o A217014     n+=1
%o A217014     if grid[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217014         return
%o A217014 while 1:
%o A217014     walk(1,  1, -1,  0)    # down-right
%o A217014     walk(-1, 0,  1, -1)    # left
%o A217014     walk(-1, 0,  1, -1)    # left
%o A217014     if posX<2:
%o A217014         break
%o A217014     walk(1, -1,  1,  1)    # up-right
%o A217014 import sys
%o A217014 grid2 = [0] * (SIZE*SIZE)
%o A217014 posX = posY = SIZE//2
%o A217014 grid2[posY*SIZE+posX]=1
%o A217014 def walk2(stepX, stepY, chkX, chkY):
%o A217014   global posX, posY
%o A217014   while 1:
%o A217014     a = grid[posY*SIZE+posX]
%o A217014     if a==0:
%o A217014         sys.exit(1)
%o A217014     print(a, end=', ')
%o A217014     posX+=stepX
%o A217014     posY+=stepY
%o A217014     grid2[posY*SIZE+posX]=1
%o A217014     if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217014         return
%o A217014 while 1:
%o A217014     walk2(0, -1, 1, 0)    # up
%o A217014     walk2(1, 0, 0, 1)     # right
%o A217014     walk2(0, 1, -1, 0)    # down
%o A217014     walk2(-1, 0, 0, -1)   # left
%Y A217014 Cf. A090861, A214526, A214226, A217010.
%K A217014 nonn,easy
%O A217014 1,2
%A A217014 _Alex Ratushnyak_, Sep 23 2012