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A217015 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of rotated-square spiral (defined in A215468).

%I A217015 #7 Mar 12 2025 18:35:47
%S A217015 1,5,6,2,8,3,10,4,12,24,13,14,27,15,7,17,31,18,9,20,35,21,11,23,39,59,
%T A217015 40,25,26,43,64,44,28,16,30,48,70,49,32,19,34,53,76,54,36,22,38,58,82,
%U A217015 110,83,60,41,42,63,88,117,89,65,45,29,47,69,95,125,96,71,50
%N A217015 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of rotated-square spiral (defined in A215468).
%o A217015 (Python)
%o A217015 SIZE = 33       # must be 4k+1
%o A217015 grid = [0] * (SIZE*SIZE)
%o A217015 posX = posY = SIZE//2
%o A217015 grid[posY*SIZE+posX]=1
%o A217015 posX += 1
%o A217015 grid[posY*SIZE+posX]=2
%o A217015 n = 3
%o A217015 def walk(stepX, stepY, chkX, chkY):
%o A217015   global posX, posY, n
%o A217015   while 1:
%o A217015     posX+=stepX
%o A217015     posY+=stepY
%o A217015     grid[posY*SIZE+posX]=n
%o A217015     n+=1
%o A217015     if grid[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217015         return
%o A217015 while posX!=SIZE-1:
%o A217015     walk(-1,  1, -1, -1)    # down-left
%o A217015     walk(-1, -1,  1, -1)    # up-left
%o A217015     walk( 1, -1,  1,  0)    # up-right
%o A217015     walk( 1,  0,  1,  1)    # right
%o A217015     walk( 1,  1, -1,  1)    # down-right
%o A217015 import sys
%o A217015 grid2 = [0] * (SIZE*SIZE)
%o A217015 posX = posY = SIZE//2
%o A217015 grid2[posY*SIZE+posX]=1
%o A217015 def walk2(stepX, stepY, chkX, chkY):
%o A217015   global posX, posY
%o A217015   while 1:
%o A217015     a = grid[posY*SIZE+posX]
%o A217015     if a==0:
%o A217015         sys.exit(1)
%o A217015     print(a, end=', ')
%o A217015     posX+=stepX
%o A217015     posY+=stepY
%o A217015     grid2[posY*SIZE+posX]=1
%o A217015     if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217015         return
%o A217015 while 1:
%o A217015     walk2(0, -1, 1, 0)    # up
%o A217015     walk2(1, 0, 0, 1)     # right
%o A217015     walk2(0, 1, -1, 0)    # down
%o A217015     walk2(-1, 0, 0, -1)   # left
%Y A217015 Cf. A090861, A214526, A215468, A217010.
%K A217015 nonn,easy
%O A217015 1,2
%A A217015 _Alex Ratushnyak_, Sep 23 2012