A217295 Permutation of natural numbers arising from applying the walk of triangular horizontal-last spiral (defined in A214226) to the data of square spiral (e.g. A214526).

1, 5, 6, 7, 22, 8, 2, 4, 16, 36, 17, 18, 19, 20, 21, 44, 75, 45, 23, 9, 11, 3, 15, 35, 63, 99, 64, 37, 38, 39, 40, 41, 42, 43, 74, 113, 160, 114, 76, 46, 24, 10, 28, 12, 14, 34, 62, 98, 142, 194, 143, 100, 65, 66, 67, 68, 69, 70, 71, 72, 73, 112, 159, 214, 277

Offset

1,2

Links

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

Prog

(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,
    posX+=stepX
    posY+=stepY
    grid2[posY*SIZE+posX]=1
    if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
        return
while 1:
    walk2(1,  1, -1,  0)    # down-right
    walk2(-1, 0,  1, -1)    # left
    walk2(-1, 0,  1, -1)    # left
    if posX<2:
        break
    walk2(1, -1,  1,  1)    # up-right

Crossrefs

Cf. A214226, A214526, A217014.

Sequence in context: A221175 A048007 A273402 * A272676 A066876 A048042

Adjacent sequences: A217292 A217293 A217294 * A217296 A217297 A217298

Keyword

nonn

Author

Alex Ratushnyak, Sep 30 2012

Status

approved