A217292 Permutation of natural numbers arising from applying the walk of right triangular type-2 spiral (defined in A214251) to the data of square spiral (e.g. A214526).

1, 8, 9, 10, 2, 4, 16, 5, 6, 7, 22, 23, 24, 25, 26, 51, 27, 11, 3, 15, 35, 63, 36, 17, 18, 19, 20, 21, 44, 45, 46, 47, 48, 49, 50, 83, 124, 84, 52, 28, 12, 14, 34, 62, 98, 142, 99, 64, 37, 38, 39, 40, 41, 42, 43, 74, 75, 76, 77, 78, 79, 80, 81, 82, 123, 172, 229

Offset

1,2

Links

Table of n, a(n) for n=1..67.

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

Crossrefs

Cf. A214251, A214526, A217011.

Sequence in context: A256923 A347219 A320304 * A004164 A004449 A168098

Adjacent sequences: A217289 A217290 A217291 * A217293 A217294 A217295

Keyword

nonn

Author

Alex Ratushnyak, Sep 30 2012

Status

approved