cp's OEIS Frontend

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.

%I A308776 #13 Jun 25 2019 01:40:19
%S A308776 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,
%T A308776 37,42,23,28,33,38,43,14,19,24,29,25,30,35,40,45,50,46,51,56,47,52,57,
%U A308776 62,67,72,77,48,53,58,63,68,73,78,34,39,44,49,54,59,55
%N 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.
%C A308776 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.
%C A308776 This sequence appears to be a permutation of the natural numbers.
%C A308776 This sequence has similarities with A308505.
%H A308776 Rémy Sigrist, <a href="/A308776/b308776.txt">Table of n, a(n) for n = 1..10201</a>
%H A308776 Rémy Sigrist, <a href="/A308776/a308776.png">Colored representation of the spiral for -500 <= x <= 500 and -500 <= y <= 500</a> (where the color is function of a(n) mod 5)
%H A308776 Rémy Sigrist, <a href="/A308776/a308776_1.png">Colored scatterplot of (n, a(n)-n) for n = 1..40401</a> (where the color is function of a(n) mod 5)
%H A308776 Rémy Sigrist, <a href="/A308776/a308776.gp.txt">PARI program for A308776</a>
%e A308776 The spiral begins:
%e A308776    89---84---79---74---69---64--123--118--113--108--103
%e A308776     |                                                 |
%e A308776    94   54---49---44---39---34---78---73---68---63   98
%e A308776     |    |                                       |    |
%e A308776    99   59   29---24---19---14---43---38---33   58   93
%e A308776     |    |    |                             |    |    |
%e A308776    95   55   25   15---10----9---18---13   28   53   88
%e A308776     |    |    |    |                   |    |    |    |
%e A308776   100   60   30   20    5----4----3    8   23   48   83
%e A308776     |    |    |    |    |         |    |    |    |    |
%e A308776   105   65   35   21    6    1----2   17   42   77  112
%e A308776     |    |    |    |    |              |    |    |    |
%e A308776   110   70   40   26   11---16----7---12   37   72  107
%e A308776     |    |    |    |                        |    |    |
%e A308776   115   75   45   31---36---41---22---27---32   67  102
%e A308776     |    |    |                                  |    |
%e A308776   120   80   50---46---51---56---47---52---57---62   97
%e A308776     |    |                                            |
%e A308776   125   85---90---61---66---71---76---81---82---87---92
%e A308776     |
%e A308776   130--135--140---86---91---96--101--106--111--116--117
%o A308776 (PARI) See Links section.
%Y A308776 Cf. A010874, A308505.
%K A308776 nonn
%O A308776 1,2
%A A308776 _Rémy Sigrist_, Jun 24 2019