cp's OEIS Frontend

A361702 Lexicographically earliest sequence of positive numbers on a square spiral such that no four equal numbers lie on the circumference of a circle.

%I A361702 #16 Apr 04 2023 07:46:55
%S A361702 1,1,1,2,1,2,1,2,2,2,1,3,3,1,3,3,3,2,2,3,2,4,4,4,2,1,2,3,4,3,4,4,5,5,
%T A361702 5,5,1,1,5,4,3,4,6,5,6,6,4,3,2,1,5,4,1,6,3,4,2,5,6,5,6,7,6,7,3,1,5,7,
%U A361702 7,6,4,6,5,7,6,4,7,8,7,6,7,4,7,5,8,8,8,6,3,6,4,8,5,8,9,9,7,8,3
%N A361702 Lexicographically earliest sequence of positive numbers on a square spiral such that no four equal numbers lie on the circumference of a circle.
%C A361702 The first term a(1) = 1 lies at the (0,0) origin while all other terms lie on integer coordinates.
%H A361702 Scott R. Shannon, <a href="/A361702/b361702.txt">Table of n, a(n) for n = 1..10000</a>
%H A361702 Scott R. Shannon, <a href="/A361702/a361702.png">Image of the first 10000 terms on the square spiral</a>. The values are scaled across the spectrum from red to violet to show their relative size. Zoom in to see the numbers.
%H A361702 Scott R. Shannon, <a href="/A361702/a361702_1.png">Image highlighting the 1 valued terms in the first 10000 terms on the square spiral</a>. Zoom in to see the numbers.
%e A361702 a(4) = 2 as a(1) = a(2) = a(3) = 1 all lie on the circumference of a circle with radius 1/sqrt(2) centered at (1/2,1/2), assuming a counter-clockwise spiral, so a(4) cannot be 1.
%e A361702 a(12) = 3 as a(2) = a(3) = a(11) = 1 all lie on the circumference of a circle with radius 1/sqrt(2) centered at (3/2,1/2), so a(12) cannot be 1, while a(4) = a(8) = a(10) = 2 all lie on the circumference of a circle with radius sqrt(2) centered at (1,0), so a(12) cannot be 2.
%e A361702 a(22) = 4 as a(1) = a(2) = a(7) = 1 all lie on the circumference of a circle with radius sqrt(10)/2 centered at (1/2,-3/2), so a(22) cannot be 1, a(6) = a(19) = a(21) = 2 all lie on the circumference of a circle with radius sqrt(5)/2 centered at (-3/2,-1), so a(22) cannot be 2, while a(12) = a(16) = a(20) = 3 all lie on the circumference of a circle with radius sqrt(5) centered at (0,0), so a(22) cannot be 3.
%Y A361702 Cf. A361486, A274640, A229037, A174344, A274923, A346294.
%K A361702 nonn
%O A361702 1,4
%A A361702 _Scott R. Shannon_, Mar 21 2023