A217296 Permutation of natural numbers arising from applying the walk of rotated-square spiral (defined in A215468) to the data of square spiral (e.g. A214526).

1, 4, 6, 8, 2, 3, 15, 5, 19, 7, 23, 9, 11, 12, 14, 34, 16, 18, 40, 20, 22, 46, 24, 10, 28, 29, 13, 33, 61, 35, 17, 39, 69, 41, 21, 45, 77, 47, 25, 27, 53, 54, 30, 32, 60, 96, 62, 36, 38, 68, 106, 70, 42, 44, 76, 116, 78, 48, 26, 52, 86, 87, 55, 31, 59, 95, 139

Offset: 1

Author

Alex Ratushnyak, Sep 30 2012

Keywords

• nonn

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A215468, A214526, A217015.

Programs

Python

SIZE = 29    # must be 4k+1
grid = [0] * (SIZE*SIZE)
posX = posY = SIZE//2
grid[posY*SIZE+posX]=1
n = 2
def walk(stepX, stepY, chkX, chkY):
  global posX, posY, n
  while 1:
    posX+=stepX
    posY+=stepY
    grid[posY*SIZE+posX]=n
    n+=1
    if grid[(posY+chkY)*SIZE+posX+chkX]==0:
        return
while posX:
    walk(0, -1, 1, 0)    # up
    walk(1, 0, 0, 1)     # right
    walk(0, 1, -1, 0)    # down
    walk(-1, 0, 0, -1)   # left
grid2 = [0] * (SIZE*SIZE)
posY = SIZE//2
posX = posY+1
grid2[posY*SIZE+posX-1] = grid2[posY*SIZE+posX] = 1
print(1, end=',')
def walk2(stepX, stepY, chkX, chkY):
  global posX, posY
  while 1:
    a = grid[posY*SIZE+posX]
    if a==0:
        raise ValueError
    print(a, end=',')
    posX+=stepX
    posY+=stepY
    grid2[posY*SIZE+posX]=1
    if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
        return
while posX!=SIZE-1:
    walk2(-1,  1, -1, -1)    # down-left
    walk2(-1, -1,  1, -1)    # up-left
    walk2( 1, -1,  1,  0)    # up-right
    walk2( 1,  0,  1,  1)    # right
    walk2( 1,  1, -1,  1)    # down-right