%I #48 Aug 24 2020 23:22:50
%S 0,1,1,1,2,2,5,1,8,8,5,17,1,26,0,29,5,25,25,18,34,5,50,1,49,17,18,52,
%T 5,85,2,90,18,61,125,13,148,10,153,20,98,125,41,145,4,148,18,85,170,
%U 18,225,148,202,173,61,197,41,226,10,229,25,117,170,5,208,80
%N a(n) is the squared distance to the origin of the n-th vertex on an acute angled Babylonian spiral.
%C An acute angled Babylonian spiral is constructed by starting with a zero vector and progressively concatenating the next longest vector with integral endpoints on a Cartesian grid. (The squares of the lengths of these vectors are A001481.) The direction of the new vector is chosen to maximize the change in direction from the previous vector. The Babylonian spiral (A256111) minimizes this angle.
%H John Bailey, <a href="/A337293/b337293.txt">Table of n, a(n) for n = 0..10000</a>
%H John Bailey, Illustrations of <a href="/A337293/a337293.png">10</a>, <a href="/A337293/a337293_1.png">100</a>, <a href="/A337293/a337293_2.png">1000</a>, <a href="/A337293/a337293_3.png">10000</a>, <a href="/A337293/a337293_4.png">100000</a>, <a href="/A337293/a337293_5.png">1500000</a>, <a href="/A337293/a337293_6.png">10000000</a>
%H John Bailey, <a href="/A337293/a337293.py.txt">Plots</a>
%F a(n) = A337311(n)^2 + A337312(n)^2.
%e The coordinates of the first few points are (0,0), (0,1), (1,0), (-1,0), (1,1), (-1,-1), (-1,2).
%o (Python) See link
%Y x-coordinates given in A337311. y-coordinates given in A337312.
%Y Cf. A001481, A256111.
%K nonn
%O 0,5
%A _John Bailey_, Aug 21 2020