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).

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, 40, 25, 26, 43, 64, 44, 28, 16, 30, 48, 70, 49, 32, 19, 34, 53, 76, 54, 36, 22, 38, 58, 82, 110, 83, 60, 41, 42, 63, 88, 117, 89, 65, 45, 29, 47, 69, 95, 125, 96, 71, 50

Offset: 1

Author

Alex Ratushnyak, Sep 23 2012

Keywords

• nonn
• easy

Crossrefs

Cf. A090861, A214526, A215468, A217010.

Programs

Python

SIZE = 33       # must be 4k+1
grid = [0] * (SIZE*SIZE)
posX = posY = SIZE//2
grid[posY*SIZE+posX]=1
posX += 1
grid[posY*SIZE+posX]=2
n = 3
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!=SIZE-1:
    walk(-1,  1, -1, -1)    # down-left
    walk(-1, -1,  1, -1)    # up-left
    walk( 1, -1,  1,  0)    # up-right
    walk( 1,  0,  1,  1)    # right
    walk( 1,  1, -1,  1)    # down-right
import sys
grid2 = [0] * (SIZE*SIZE)
posX = posY = SIZE//2
grid2[posY*SIZE+posX]=1
def walk2(stepX, stepY, chkX, chkY):
  global posX, posY
  while 1:
    a = grid[posY*SIZE+posX]
    if a==0:
        sys.exit(1)
    print(a, end=', ')
    posX+=stepX
    posY+=stepY
    grid2[posY*SIZE+posX]=1
    if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
        return
while 1:
    walk2(0, -1, 1, 0)    # up
    walk2(1, 0, 0, 1)     # right
    walk2(0, 1, -1, 0)    # down
    walk2(-1, 0, 0, -1)   # left