A217013 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of triangular horizontal-first spiral (defined in A214250).

1, 3, 14, 4, 6, 7, 8, 2, 12, 30, 13, 32, 59, 33, 15, 5, 19, 20, 21, 22, 23, 9, 11, 29, 55, 89, 56, 31, 58, 93, 136, 94, 60, 34, 16, 18, 40, 41, 42, 43, 44, 45, 46, 24, 10, 28, 54, 88, 130, 180, 131, 90, 57, 92, 135, 186, 245, 187, 137, 95, 61, 35, 17, 39, 69

Offset

1,2

Links

Table of n, a(n) for n=1..65.

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 posX<SIZE-2:
    walk(-1, 0,  1, -1)    # left
    walk(1, -1,  1,  1)    # up-right
    walk(1,  1, -1,  0)    # down-right
    walk(-1, 0,  1, -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,
    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, A214250, A217010.

Sequence in context: A147584 A163357 A179087 * A058991 A341860 A197423

Adjacent sequences: A217010 A217011 A217012 * A217014 A217015 A217016

Keyword

nonn,easy

Author

Alex Ratushnyak, Sep 23 2012

Status

approved