cp's OEIS Frontend

A357985 Counterclockwise square spiral constructed using the integers so that a(n) plus all other numbers currently visible from the current number equals n; start with a(0) = 0.

%I A357985 #43 Apr 13 2023 06:08:55
%S A357985 0,1,1,1,2,1,3,-1,6,-2,-1,0,1,9,-8,15,-5,-7,-10,14,-29,58,-78,101,
%T A357985 -118,150,-61,309,-307,553,-494,-186,-644,315,-1177,731,-1458,3480,
%U A357985 -5183,7096,-8328,9735,-10882,7200,-29452,31322,-52670,51401,-65210,61001,11318,135012,-109687,259226,-221542
%N A357985 Counterclockwise square spiral constructed using the integers so that a(n) plus all other numbers currently visible from the current number equals n; start with a(0) = 0.
%C A357985 A number is visible from the current number if, given that it has coordinates (x,y) relative to the current number, the greatest common divisor of |x| and |y| is 1.
%C A357985 The magnitude of the numbers grow surprisingly quickly, e.g., a(150) = -4346232663618226. The only known terms that equal zero are a(0) and a(11); it is unknown whether more exist or if all integers eventually appear.
%e A357985 The spiral begins:
%e A357985 .
%e A357985                                  .
%e A357985                                  .
%e A357985     -5....15...-8....9.....1    553
%e A357985      |                     |     |
%e A357985     -7    2....1.....1     0   -307
%e A357985      |    |          |     |     |
%e A357985    -10    1    0.....1    -1    309
%e A357985      |    |                |     |
%e A357985     14    3...-1.....6... -2    -61
%e A357985      |                           |
%e A357985    -29...58...-78...101...-118...150
%e A357985 .
%e A357985 .
%e A357985 a(6) = 3 as from square 6, at (-1,1) relative to the starting square, the numbers currently visible are 1 (at -1,0), 0 (at 0,0), 1 (at 0,1), and 1 (at 1,0). These four numbers sum to 3, so a(6) = 3 so that 3 + 3 = 6.
%e A357985 a(7) = -1 as from square 7, at (0,-1) relative to the starting square, the numbers currently visible are 3 (at -1,-1), 1 (at -1,0), 2 (at -1,1), 0 (at 0,0), 1 (at 1,1), and 1 (at 1,0). These six numbers sum to 8, so a(7) = -1 so that -1 + 8 = 7.
%Y A357985 Cf. A357991, A307834, A275609, A274640, A355270.
%K A357985 sign
%O A357985 0,5
%A A357985 _Scott R. Shannon_, Oct 23 2022