A214526 -id:A214526 - cp's OEIS frontend

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

Alex Ratushnyak, Sep 23 2012

			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

Cf. A090861, A214526, A214230.

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

A217015 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of rotated-square spiral (defined in A215468).

Original entry on oeis.org

1, 5, 6, 2, 8, 3, 10, 4, 12, 24, 13, 14, 27, 15, 7, 17, 31, 18, 9, 20, 35, 21, 11, 23, 39, 59, 40, 25, 26, 43, 64, 44, 28, 16, 30, 48, 70, 49, 32, 19, 34, 53, 76, 54, 36, 22, 38, 58, 82, 110, 83, 60, 41, 42, 63, 88, 117, 89, 65, 45, 29, 47, 69, 95, 125, 96, 71, 50

Offset: 1

Alex Ratushnyak, Sep 23 2012

Cf. A090861, A214526, A215468, A217010.

SIZE = 33       # must be 4k+1
grid = [0] * (SIZE*SIZE)
posX = posY = SIZE//2
grid[posY*SIZE+posX]=1
posX += 1
grid[posY*SIZE+posX]=2
n = 3
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!=SIZE-1:
    walk(-1,  1, -1, -1)    # down-left
    walk(-1, -1,  1, -1)    # up-left
    walk( 1, -1,  1,  0)    # up-right
    walk( 1,  0,  1,  1)    # right
    walk( 1,  1, -1,  1)    # down-right
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 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

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).

Original entry on oeis.org

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

Alex Ratushnyak, Sep 23 2012

Cf. A090861, A214526, A214251, A217010.

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, end=', ')
    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

A217012 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of right triangular type-3 spiral (defined in A214252).

Original entry on oeis.org

1, 8, 25, 9, 2, 3, 4, 5, 6, 7, 24, 50, 85, 51, 26, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 49, 84, 128, 181, 129, 86, 52, 27, 11, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 22, 48, 83, 127, 180, 242

Offset: 1

Alex Ratushnyak, Sep 23 2012

Cf. A090861, A214526, A214252, A217010.

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 posY!=0:
    walk( 1, 1, -1,  0)    # right-down
    walk(-1, 0,  0, -1)    # left
    walk(0, -1,  1,  1)    # up
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 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

A217013 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of triangular horizontal-first spiral (defined in A214250).

Original entry on oeis.org

1, 3, 14, 4, 6, 7, 8, 2, 12, 30, 13, 32, 59, 33, 15, 5, 19, 20, 21, 22, 23, 9, 11, 29, 55, 89, 56, 31, 58, 93, 136, 94, 60, 34, 16, 18, 40, 41, 42, 43, 44, 45, 46, 24, 10, 28, 54, 88, 130, 180, 131, 90, 57, 92, 135, 186, 245, 187, 137, 95, 61, 35, 17, 39, 69

Offset: 1

Alex Ratushnyak, Sep 23 2012

Cf. A090861, A214526, A214250, A217010.

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 posX

A217014 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of triangular horizontal-last spiral (defined in A214226).

Original entry on oeis.org

1, 7, 22, 8, 2, 3, 4, 6, 20, 42, 21, 44, 75, 45, 23, 9, 11, 12, 13, 14, 15, 5, 19, 41, 71, 109, 72, 43, 74, 113, 160, 114, 76, 46, 24, 10, 28, 29, 30, 31, 32, 33, 34, 16, 18, 40, 70, 108, 154, 208, 155, 110, 73, 112, 159, 214

Offset: 1

Alex Ratushnyak, Sep 23 2012

Cf. A090861, A214526, A214226, A217010.

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,  1, -1,  0)    # down-right
    walk(-1, 0,  1, -1)    # left
    walk(-1, 0,  1, -1)    # left
    if posX<2:
        break
    walk(1, -1,  1,  1)    # up-right
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 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

A217296 Permutation of natural numbers arising from applying the walk of rotated-square spiral (defined in A215468) to the data of square spiral (e.g. A214526).

Original entry on oeis.org

1, 4, 6, 8, 2, 3, 15, 5, 19, 7, 23, 9, 11, 12, 14, 34, 16, 18, 40, 20, 22, 46, 24, 10, 28, 29, 13, 33, 61, 35, 17, 39, 69, 41, 21, 45, 77, 47, 25, 27, 53, 54, 30, 32, 60, 96, 62, 36, 38, 68, 106, 70, 42, 44, 76, 116, 78, 48, 26, 52, 86, 87, 55, 31, 59, 95, 139

Offset: 1

Alex Ratushnyak, Sep 30 2012

nonn

Index entries for sequences that are permutations of the natural numbers

Cf. A215468, A214526, A217015.

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
grid2 = [0] * (SIZE*SIZE)
posY = SIZE//2
posX = posY+1
grid2[posY*SIZE+posX-1] = grid2[posY*SIZE+posX] = 1
print(1, end=',')
def walk2(stepX, stepY, chkX, chkY):
  global posX, posY
  while 1:
    a = grid[posY*SIZE+posX]
    if a==0:
        raise ValueError
    print(a, end=',')
    posX+=stepX
    posY+=stepY
    grid2[posY*SIZE+posX]=1
    if grid2[(posY+chkY)*SIZE+posX+chkX]==0:
        return
while posX!=SIZE-1:
    walk2(-1,  1, -1, -1)    # down-left
    walk2(-1, -1,  1, -1)    # up-left
    walk2( 1, -1,  1,  0)    # up-right
    walk2( 1,  0,  1,  1)    # right
    walk2( 1,  1, -1,  1)    # down-right

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).

Original entry on oeis.org

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

Alex Ratushnyak, Sep 30 2012

nonn

Cf. A214230, A214526, A217010.

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, end=', ')
    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

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).

Original entry on oeis.org

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

Alex Ratushnyak, Sep 30 2012

nonn

Cf. A214251, A214526, A217011.

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, end=', ')
    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

A217293 Permutation of natural numbers arising from applying the walk of right triangular type-3 spiral (defined in A214252) to the data of square spiral (e.g. A214526).

Original entry on oeis.org

1, 5, 6, 7, 8, 9, 10, 2, 4, 16, 36, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 51, 27, 11, 3, 15, 35, 63, 99, 64, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 83, 124, 84, 52, 28, 12, 14, 34, 62, 98, 142, 194, 143, 100, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Alex Ratushnyak, Sep 30 2012

nonn

Cf. A214252, A214526, A217012.

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

cp's OEIS Frontend

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).

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A217015 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of rotated-square spiral (defined in A215468).

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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).

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A217012 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of right triangular type-3 spiral (defined in A214252).

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A217013 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of triangular horizontal-first spiral (defined in A214250).

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A217014 Permutation of natural numbers arising from applying the walk of a square spiral (e.g. A214526) to the data of triangular horizontal-last spiral (defined in A214226).

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A217296 Permutation of natural numbers arising from applying the walk of rotated-square spiral (defined in A215468) to the data of square spiral (e.g. A214526).

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Python

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).

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Python

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).

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Python

A217293 Permutation of natural numbers arising from applying the walk of right triangular type-3 spiral (defined in A214252) to the data of square spiral (e.g. A214526).

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Python