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A217291 Permutation of natural numbers arising from applying the walk of right triangular type-1 spiral (defined in A214230) to the data of square spiral (e.g. A214526).

%I A217291 #11 Mar 12 2025 20:14:56
%S A217291 1,2,4,16,5,6,7,8,9,10,27,11,3,15,35,63,36,17,18,19,20,21,22,23,24,25,
%T A217291 26,51,84,52,28,12,14,34,62,98,142,99,64,37,38,39,40,41,42,43,44,45,
%U A217291 46,47,48,49,50,83,124,173,125,85,53,29,13,33,61,97,141,193,253
%N A217291 Permutation of natural numbers arising from applying the walk of right triangular type-1 spiral (defined in A214230) to the data of square spiral (e.g. A214526).
%o A217291 (Python)
%o A217291 SIZE = 29    # must be 4k+1
%o A217291 grid = [0] * (SIZE*SIZE)
%o A217291 posX = posY = SIZE//2
%o A217291 grid[posY*SIZE+posX]=1
%o A217291 n = 2
%o A217291 def walk(stepX, stepY, chkX, chkY):
%o A217291   global posX, posY, n
%o A217291   while 1:
%o A217291     posX+=stepX
%o A217291     posY+=stepY
%o A217291     grid[posY*SIZE+posX]=n
%o A217291     n+=1
%o A217291     if grid[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217291         return
%o A217291 while posX:
%o A217291     walk(0, -1, 1, 0)    # up
%o A217291     walk(1, 0, 0, 1)     # right
%o A217291     walk(0, 1, -1, 0)    # down
%o A217291     walk(-1, 0, 0, -1)   # left
%o A217291 import sys
%o A217291 grid2 = [0] * (SIZE*SIZE)
%o A217291 posX = posY = SIZE//2
%o A217291 grid2[posY*SIZE+posX]=1
%o A217291 def walk2(stepX, stepY, chkX, chkY):
%o A217291   global posX, posY
%o A217291   while 1:
%o A217291     a = grid[posY*SIZE+posX]
%o A217291     if a==0:
%o A217291         sys.exit(1)
%o A217291     print(a, end=', ')
%o A217291     posX+=stepX
%o A217291     posY+=stepY
%o A217291     grid2[posY*SIZE+posX]=1
%o A217291     if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217291         return
%o A217291 while 1:
%o A217291     walk2(0, -1,  1,  1)    # up
%o A217291     walk2( 1, 1, -1,  0)    # right-down
%o A217291     if posX==SIZE-1:
%o A217291         break
%o A217291     walk2(-1, 0,  0, -1)    # left
%Y A217291 Cf. A214230, A214526, A217010.
%K A217291 nonn
%O A217291 1,2
%A A217291 _Alex Ratushnyak_, Sep 30 2012