A217011 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of right triangular type-2 spiral (defined in A214251).

1, 5, 19, 6, 8, 9, 10, 2, 3, 4, 18, 41, 73, 42, 20, 7, 24, 25, 26, 27, 28, 11, 12, 13, 14, 15, 17, 40, 72, 113, 163, 114, 74, 43, 21, 23, 49, 50, 51, 52, 53, 54, 55, 29, 30, 31, 32, 33, 34, 35, 16, 39, 71, 112, 162, 221

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, 0,  0, -1)    # left
    walk(0, -1,  1,  1)    # up
    if posY==0:
        break
    walk( 1, 1, -1,  0)    # right-down
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, A214251, A217010.

Sequence in context: A274995 A370491 A089082 * A106229 A129734 A109325

Adjacent sequences: A217008 A217009 A217010 * A217012 A217013 A217014

Keyword

nonn,easy

Author

Alex Ratushnyak, Sep 23 2012

Status

approved