A217293 Permutation of natural numbers arising from applying the walk of right triangular type-3 spiral (defined in A214252) to the data of square spiral (e.g. A214526).

1, 5, 6, 7, 8, 9, 10, 2, 4, 16, 36, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 51, 27, 11, 3, 15, 35, 63, 99, 64, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 83, 124, 84, 52, 28, 12, 14, 34, 62, 98, 142, 194, 143, 100, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Alex Ratushnyak, Sep 30 2012

Keywords

• nonn

Crossrefs

Cf. A214252, A214526, A217012.

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
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 posY!=0:
    walk2( 1, 1, -1,  0)    # right-down
    walk2(-1, 0,  0, -1)    # left
    walk2(0, -1,  1,  1)    # up