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A308505 Counterclockwise square spiral of distinct positive integers constructed by greedy algorithm, such that for p = 2 and 3, every multiple of p (except p itself) is vertically or horizontally adjacent to a cell already holding a multiple of p.

%I A308505 #13 Jun 03 2019 09:14:38
%S A308505 1,2,3,5,7,11,13,17,4,8,10,6,9,15,19,23,25,29,31,35,37,41,43,14,16,20,
%T A308505 22,26,12,18,21,27,33,39,45,47,49,53,55,59,61,65,67,71,73,77,28,32,34,
%U A308505 38,40,44,46,24,30,36,42,48,50,51,57,63,69,75,79,83,85
%N A308505 Counterclockwise square spiral of distinct positive integers constructed by greedy algorithm, such that for p = 2 and 3, every multiple of p (except p itself) is vertically or horizontally adjacent to a cell already holding a multiple of p.
%C A308505 For p = 2 and 3, the set S_p of lattice points holding a multiple of p is connected with respect to von Neumann neighborhood and has interesting graphical features (see representation in Links section).
%C A308505 Apparently this sequence is a permutation of the natural number with infinitely many fixed points.
%H A308505 Rémy Sigrist, <a href="/A308505/a308505.png">Representation of S_2 restricted to -500 <= x <= +500 and -500 <= y <= +500</a>
%H A308505 Rémy Sigrist, <a href="/A308505/a308505_1.png">Representation of S_3 restricted to -500 <= x <= +500 and -500 <= y <= +500</a>
%H A308505 Rémy Sigrist, <a href="/A308505/a308505_2.png">Colored representation of (a(n)-n) restricted to -500 <= x <= +500 and -500 <= y <= +500</a> (where black pixels correspond to zeros, blue shades correspond to negative values and red shades correspond to positive values)
%H A308505 Rémy Sigrist, <a href="/A308505/a308505.gp.txt">PARI program for A308505</a>
%e A308505 The spiral begins:
%e A308505   111--105---99---93---87---86---84---82---81---80---78
%e A308505     |                                                 |
%e A308505   117   79---75---69---63---57---51---50---48---42   72
%e A308505     |    |                                       |    |
%e A308505   119   83   49---47---45---39---33---27---21   36   66
%e A308505     |    |    |                             |    |    |
%e A308505   121   85   53   25---23---19---15----9   18   30   60
%e A308505     |    |    |    |                   |    |    |    |
%e A308505   125   89   55   29    7----5----3    6   12   24   54
%e A308505     |    |    |    |    |         |    |    |    |    |
%e A308505   127   91   59   31   11    1----2   10   26   46   76
%e A308505     |    |    |    |    |              |    |    |    |
%e A308505   131   95   61   35   13---17----4----8   22   44   74
%e A308505     |    |    |    |                        |    |    |
%e A308505   133   97   65   37---41---43---14---16---20   40   70
%e A308505     |    |    |                                  |    |
%e A308505   137  101   67---71---73---77---28---32---34---38   68
%e A308505     |    |                                            |
%e A308505   139  103--107--109--113--115---52---56---58---62---64
%e A308505     |
%e A308505   143--145--149--151--155--157---88---92---94---98--100
%o A308505 (PARI) See Links section.
%Y A308505 Cf. A005843, A008585.
%K A308505 nonn
%O A308505 1,2
%A A308505 _Rémy Sigrist_, Jun 02 2019