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

1,2

Links

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

Example

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

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(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,
    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

Crossrefs

Cf. A090861, A214526, A214230.

Sequence in context: A089778 A088253 A249224 * A091023 A337838 A120863

Adjacent sequences: A217007 A217008 A217009 * A217011 A217012 A217013

Keyword

nonn,easy

Author

Alex Ratushnyak, Sep 23 2012

Status

approved