|
%I #15 Feb 12 2020 16:18:15
%S 0,0,1,1,0,0,1,1,2,2,3,3,4,4,3,3,2,2,1,1,0,0,1,1,0,0,1,1,2,2,3,3,2,2,
%T 3,3,4,4,5,5,6,6,7,7,6,6,7,7,8,8,9,9,10,10,9,9,10,10,11,11,12,12,13,
%U 13,12,12,11,11,10,10,9,9,10,10,9,9,8,8,7,7,6
%N a(n) is the Y-coordinate of the n-th point of the quadratic Koch curve. Sequence A332249 gives X-coordinates.
%C This sequence is the imaginary part of {f(n)} defined as:
%C - f(0) = 0,
%C - f(n+1) = f(n) + i^t(n)
%C where t(n) is the number of 1's minus the number of 3's
%C in the base 5 representation of n
%C and i denotes the imaginary unit.
%H Rémy Sigrist, <a href="/A332250/b332250.txt">Table of n, a(n) for n = 0..15625</a>
%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F a(5^k-m) = a(m) for any k >= 0 and m = 0..5^k.
%o (PARI) { k = [0, 1, 0, -1, 0]; z=0; for (n=0, 80, print1 (imag(z) ", "); z += I^vecsum(apply(d -> k[1+d], digits(n, #k)))) }
%Y Cf. A332249 (X-coordinates and additional comments).
%K nonn,base
%O 0,9
%A _Rémy Sigrist_, Feb 08 2020
|
