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A217292 Permutation of natural numbers arising from applying the walk of right triangular type-2 spiral (defined in A214251) to the data of square spiral (e.g. A214526).

%I A217292 #8 Nov 05 2024 18:57:26
%S A217292 1,8,9,10,2,4,16,5,6,7,22,23,24,25,26,51,27,11,3,15,35,63,36,17,18,19,
%T A217292 20,21,44,45,46,47,48,49,50,83,124,84,52,28,12,14,34,62,98,142,99,64,
%U A217292 37,38,39,40,41,42,43,74,75,76,77,78,79,80,81,82,123,172,229
%N A217292 Permutation of natural numbers arising from applying the walk of right triangular type-2 spiral (defined in A214251) to the data of square spiral (e.g. A214526).
%o A217292 (Python)
%o A217292 SIZE = 29    # must be 4k+1
%o A217292 grid = [0] * (SIZE*SIZE)
%o A217292 posX = posY = SIZE//2
%o A217292 grid[posY*SIZE+posX]=1
%o A217292 n = 2
%o A217292 def walk(stepX, stepY, chkX, chkY):
%o A217292   global posX, posY, n
%o A217292   while 1:
%o A217292     posX+=stepX
%o A217292     posY+=stepY
%o A217292     grid[posY*SIZE+posX]=n
%o A217292     n+=1
%o A217292     if grid[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217292         return
%o A217292 while posX:
%o A217292     walk(0, -1, 1, 0)    # up
%o A217292     walk(1, 0, 0, 1)     # right
%o A217292     walk(0, 1, -1, 0)    # down
%o A217292     walk(-1, 0, 0, -1)   # left
%o A217292 import sys
%o A217292 grid2 = [0] * (SIZE*SIZE)
%o A217292 posX = posY = SIZE//2
%o A217292 grid2[posY*SIZE+posX]=1
%o A217292 def walk2(stepX, stepY, chkX, chkY):
%o A217292   global posX, posY
%o A217292   while 1:
%o A217292     a = grid[posY*SIZE+posX]
%o A217292     if a==0:
%o A217292         sys.exit(1)
%o A217292     print(a, end=', ')
%o A217292     posX+=stepX
%o A217292     posY+=stepY
%o A217292     grid2[posY*SIZE+posX]=1
%o A217292     if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217292         return
%o A217292 while 1:
%o A217292     walk2(-1, 0,  0, -1)    # left
%o A217292     walk2(0, -1,  1,  1)    # up
%o A217292     if posY==0:
%o A217292         break
%o A217292     walk2( 1, 1, -1,  0)    # right-down
%Y A217292 Cf. A214251, A214526, A217011.
%K A217292 nonn
%O A217292 1,2
%A A217292 _Alex Ratushnyak_, Sep 30 2012