A217291 Permutation of natural numbers arising from applying the walk of right triangular type-1 spiral (defined in A214230) to the data of square spiral (e.g. A214526).

1, 2, 4, 16, 5, 6, 7, 8, 9, 10, 27, 11, 3, 15, 35, 63, 36, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 51, 84, 52, 28, 12, 14, 34, 62, 98, 142, 99, 64, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 83, 124, 173, 125, 85, 53, 29, 13, 33, 61, 97, 141, 193, 253

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

Crossrefs

Cf. A214230, A214526, A217010.

Sequence in context: A097542 A277850 A332352 * A364247 A338839 A350554

Adjacent sequences: A217288 A217289 A217290 * A217292 A217293 A217294

Keyword

nonn

Author

Alex Ratushnyak, Sep 30 2012

Status

approved