login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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 (list; graph; refs; listen; history; text; internal format)
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, 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)
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
Sequence in context: A221471 A058243 A264665 * A339556 A264995 A319722
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 24 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)