A217014 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of triangular horizontal-last spiral (defined in A214226).

1, 7, 22, 8, 2, 3, 4, 6, 20, 42, 21, 44, 75, 45, 23, 9, 11, 12, 13, 14, 15, 5, 19, 41, 71, 109, 72, 43, 74, 113, 160, 114, 76, 46, 24, 10, 28, 29, 30, 31, 32, 33, 34, 16, 18, 40, 70, 108, 154, 208, 155, 110, 73, 112, 159, 214

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Prog

(Python)
SIZE = 33       # 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 1:
    walk(1,  1, -1,  0)    # down-right
    walk(-1, 0,  1, -1)    # left
    walk(-1, 0,  1, -1)    # left
    if posX<2:
        break
    walk(1, -1,  1,  1)    # up-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,
    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

Crossrefs

Cf. A090861, A214526, A214226, A217010.

Sequence in context: A082826 A130740 A101119 * A200886 A070412 A286572

Adjacent sequences: A217011 A217012 A217013 * A217015 A217016 A217017

Keyword

nonn,easy

Author

Alex Ratushnyak, Sep 23 2012

Status

approved