A220098 Manhattan distances between 2n and 1 in the double spiral with positive integers and 1 at the center.

1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 7, 8, 9, 10, 11, 12, 13

Offset

1,2

Comments

Double spiral begins:

.

82---84---86---88---90---92---94---96---98

|

80 51---53---55---57---59---61---63---65

| | |

78 49 26---28---30---32---34---36 67

| | | | |

76 47 24 11---13---15---17 38 69

| | | | | | |

74 45 22 9 2----4 19 40 71

| | | | | | | | |

72 43 20 7 1 6 21 42 73

| | | | | | | | |

70 41 18 5----3 8 23 44 75

| | | | | | |

68 39 16---14---12---10 25 46 77

| | | | |

66 37---35---33---31---29---27 48 79

| | |

64---62---60---58---56---54---52---50 81

|

99---97---95---93---91---89---87---85---83

Links

Table of n, a(n) for n=1..85.

Formula

abs( a(n) - a(n-1) ) = 1.

Example

From Philippe Deléham, Mar 08 2013: (Start)
As a square array, this begins:
  1,  1,  2,  2,  3,  3,  4,  4,  5, ...
  2,  3,  3,  4,  4,  5,  5,  6,  6, ...
  2,  4,  5,  5,  6,  6,  7,  7,  8, ...
  3,  4,  6,  7,  7,  8,  8,  9,  9, ...
  3,  5,  6,  8,  9,  9, 10, 10, 11, ...
  4,  5,  7,  8, 10, 11, 11, 12, 12, ...
  4,  6,  7,  9, 10, 12, 13, 13, 14, ...
  5,  6,  8,  9, 11, 12, 14, 15, 15, ..., etc.
As a triangle, this begins:
  1
  2, 1
  2, 3, 2
  3, 4, 3, 2
  3, 4, 5, 4, 3
  4, 5, 6, 5, 4, 3, etc. (End)

Prog

(C)
#include <stdio.h>
#define SIZE 20
int grid[SIZE][SIZE];
int direction[] = {0, -1,  1, 0, 0, 1, -1, 0};
main() {
  int i, j, x1, y1, x2, y2, stepSize;
  int direction1pos=0, direction2pos=4, val;
  x1 = y1 = x2 = y2 = SIZE/2;
  for (val=grid[y1][x1]=1, stepSize=0; ; ++stepSize) {
    if (x1<1 || x1>=SIZE-1 || x2<1 || x2>=SIZE-1) break;
    if (y1<1 || y1>=SIZE-1 || y2<1 || y2>=SIZE-1) break;
    for (i=stepSize|1; i; ++val, --i) {
      x1 += direction[direction1pos  ];
      y1 += direction[direction1pos+1];
      x2 += direction[direction2pos  ];
      y2 += direction[direction2pos+1];
      grid[y1][x1] = val*2;
      grid[y2][x2] = val*2+1;
      printf("%d, ", abs(x1-SIZE/2)+abs(y1-SIZE/2));
    }
    direction1pos = (direction1pos+2) & 7;
    direction2pos = (direction2pos+2) & 7;
  }
  for (i=0; i<SIZE; ++i) {
    printf("\n");
    for (j=0; j<SIZE; ++j)
      printf("%4d ", grid[i][j]);
  }
}

Crossrefs

Cf. A077043, A214526.

Sequence in context: A033667 A033923 A233420 * A246017 A116939 A253174

Adjacent sequences: A220095 A220096 A220097 * A220099 A220100 A220101

Keyword

nonn,easy

Author

Alex Ratushnyak, Dec 04 2012

Status

approved