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A217294 Permutation of natural numbers arising from applying the walk of triangular horizontal-first spiral (defined in A214250) to the data of square spiral (e.g. A214526).

%I A217294 #7 Nov 07 2024 15:22:10
%S A217294 1,8,2,4,16,5,6,7,22,45,23,9,11,3,15,35,63,36,17,18,19,20,21,44,75,
%T A217294 114,76,46,24,10,28,12,14,34,62,98,142,99,64,37,38,39,40,41,42,43,74,
%U A217294 113,160,215,161,115,77,47,25,27,53,29,13,33,61,97,141,193,253
%N A217294 Permutation of natural numbers arising from applying the walk of triangular horizontal-first spiral (defined in A214250) to the data of square spiral (e.g. A214526).
%o A217294 (Python)
%o A217294 SIZE = 29    # must be 4k+1
%o A217294 grid = [0] * (SIZE*SIZE)
%o A217294 posX = posY = SIZE//2
%o A217294 grid[posY*SIZE+posX]=1
%o A217294 n = 2
%o A217294 def walk(stepX, stepY, chkX, chkY):
%o A217294   global posX, posY, n
%o A217294   while 1:
%o A217294     posX+=stepX
%o A217294     posY+=stepY
%o A217294     grid[posY*SIZE+posX]=n
%o A217294     n+=1
%o A217294     if grid[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217294         return
%o A217294 while posX:
%o A217294     walk(0, -1, 1, 0)    # up
%o A217294     walk(1, 0, 0, 1)     # right
%o A217294     walk(0, 1, -1, 0)    # down
%o A217294     walk(-1, 0, 0, -1)   # left
%o A217294 import sys
%o A217294 grid2 = [0] * (SIZE*SIZE)
%o A217294 posX = posY = SIZE//2
%o A217294 grid2[posY*SIZE+posX]=1
%o A217294 def walk2(stepX, stepY, chkX, chkY):
%o A217294   global posX, posY
%o A217294   while 1:
%o A217294     a = grid[posY*SIZE+posX]
%o A217294     if a==0:
%o A217294         sys.exit(1)
%o A217294     print(a, end=', ')
%o A217294     posX+=stepX
%o A217294     posY+=stepY
%o A217294     grid2[posY*SIZE+posX]=1
%o A217294     if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
%o A217294         return
%o A217294 while posX<SIZE-2:
%o A217294     walk2(-1, 0,  1, -1)    # left
%o A217294     walk2(1, -1,  1,  1)    # up-right
%o A217294     walk2(1,  1, -1,  0)    # down-right
%o A217294     walk2(-1, 0,  1, -1)    # left
%Y A217294 Cf. A214250, A214526, A217013.
%K A217294 nonn
%O A217294 1,2
%A A217294 _Alex Ratushnyak_, Sep 30 2012