A308776 Counterclockwise square spiral of distinct positive integers constructed by greedy algorithm, such that for k = 1..5, every term equal to k mod 5 (except k itself) is vertically or horizontally adjacent to a cell already holding a value equal to k mod 5.

1, 2, 3, 4, 5, 6, 11, 16, 7, 12, 17, 8, 13, 18, 9, 10, 15, 20, 21, 26, 31, 36, 41, 22, 27, 32, 37, 42, 23, 28, 33, 38, 43, 14, 19, 24, 29, 25, 30, 35, 40, 45, 50, 46, 51, 56, 47, 52, 57, 62, 67, 72, 77, 48, 53, 58, 63, 68, 73, 78, 34, 39, 44, 49, 54, 59, 55

Offset

1,2

Comments

For k = 1..5, let M_k be the set of lattice points with a value equal to k mod 5; the sets M_1, ..., M_5 form 5 arms that spiral around the origin (see representation in Links section). As a consequence, the sequence alternates runs of terms in arithmetic progression with first difference 5.

This sequence appears to be a permutation of the natural numbers.

This sequence has similarities with A308505.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10201

Rémy Sigrist, Colored representation of the spiral for -500 <= x <= 500 and -500 <= y <= 500 (where the color is function of a(n) mod 5)

Rémy Sigrist, Colored scatterplot of (n, a(n)-n) for n = 1..40401 (where the color is function of a(n) mod 5)

Rémy Sigrist, PARI program for A308776

Example

The spiral begins:
   89---84---79---74---69---64--123--118--113--108--103
    |                                                 |
   94   54---49---44---39---34---78---73---68---63   98
    |    |                                       |    |
   99   59   29---24---19---14---43---38---33   58   93
    |    |    |                             |    |    |
   95   55   25   15---10----9---18---13   28   53   88
    |    |    |    |                   |    |    |    |
  100   60   30   20    5----4----3    8   23   48   83
    |    |    |    |    |         |    |    |    |    |
  105   65   35   21    6    1----2   17   42   77  112
    |    |    |    |    |              |    |    |    |
  110   70   40   26   11---16----7---12   37   72  107
    |    |    |    |                        |    |    |
  115   75   45   31---36---41---22---27---32   67  102
    |    |    |                                  |    |
  120   80   50---46---51---56---47---52---57---62   97
    |    |                                            |
  125   85---90---61---66---71---76---81---82---87---92
    |
  130--135--140---86---91---96--101--106--111--116--117

Prog

(PARI) See Links section.

Crossrefs

Cf. A010874, A308505.

Sequence in context: A221471 A058243 A264665 * A339556 A264995 A319722

Adjacent sequences: A308773 A308774 A308775 * A308777 A308778 A308779

Keyword

nonn

Author

Rémy Sigrist, Jun 24 2019

Status

approved