A217010 Permutation of natural numbers arising from applying the walk of a square spiral (e.g., A214526) to the data of right triangular type-1 spiral (defined in A214230).

1, 2, 13, 3, 5, 6, 7, 8, 9, 10, 12, 32, 61, 33, 14, 4, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 11, 31, 60, 98, 145, 99, 62, 34, 15, 17, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 28, 30, 59, 97, 144, 200, 265, 201, 146, 100, 63, 35, 16, 39, 71

Offset: 1

Author

Alex Ratushnyak, Sep 23 2012

Keywords

• nonn
• easy

Examples

			Triangular spiral (A214230) begins:
.
  56
   | \
  55  57
   |     \
  54  29  58
   |   | \   \
  53  28  30  59
   |   |     \   \
  52  27  11  31  60
   |   |   | \   \   \
  51  26  10  12  32  61
   |   |   |     \   \   \
  50  25   9   2  13  33  62
   |   |   |   | \   \   \   \
  49  24   8   1   3  14  34  63
   |   |   |         \   \   \   \
  48  23   7---6---5---4  15  35  64
   |   |                     \   \   \
  47  22--21--20--19--18--17--16  36  65
   |                                 \   \
  46--45--44--43--42--41--40--39--38--37  66
                                             \
  78--77--76--75--74--73--72--71--70--69--68--67
.
Square spiral (defining order in which elements are fetched) begins:
.
  49  26--27--28--29--30--31
   |   |                   |
  48  25  10--11--12--13  32
   |   |   |           |   |
  47  24   9   2---3  14  33
   |   |   |   |   |   |   |
  46  23   8   1   4  15  34
   |   |   |       |   |   |
  45  22   7---6---5  16  35
   |   |               |   |
  44  21--20--19--18--17  36
   |                       |
  43--42--41--40--39--38--37
		

Crossrefs

Cf. A090861, A214526, A214230.

Programs

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