A327439 - OEIS

%I #27 Dec 17 2024 22:54:15

%S 1,3,2,1,3,2,5,4,9,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,3,

%T 2,5,4,9,13,12,11,10,9,8,7,6,5,4,3,2,1,3,2,5,4,7,6,9,8,11,23,22,21,20,

%U 19,18,17,16,15,14,13,12,11

%N a(0)=1. If a(n-1) and n are relatively prime and a(n-1)!=1, a(n) = a(n-1) - 1. Otherwise (i.e., if a(n-1) and n share a common factor or a(n-1)=1), a(n) = a(n-1) + gcd(a(n-1),n) + 1.

%C Graphically at large scales this sequence is vaguely self-similar, though in certain sections it acts in a rough manner, in particular in regions surrounding apparent cusps. See the program for a graph to zoom in on these sections.

%C See Python program for zoomable graph.

%H Nathaniel J. Strout, <a href="/A327439/b327439.txt">Table of n, a(n) for n = 0..116000</a>

%t a[0] = 1; a[n_] := a[n] = If[a[n - 1] != 1 && CoprimeQ[n, a[n - 1]], a[n - 1] - 1, a[n - 1] + GCD[a[n - 1], n] + 1]; Array[a, 101, 0] (* _Amiram Eldar_, Feb 24 2020 *)

%t nxt[{n_,a_}]:={n+1,If[CoprimeQ[n+1,a]&&a!=1,a-1,a+GCD[a,n+1]+1]}; NestList[nxt,{0,1},70][[;;,2]] (* _Harvey P. Dale_, Jun 08 2024 *)

%o (Python)

%o import math

%o import matplotlib.pyplot as plt

%o num = 10000

%o x = []

%o y = []

%o # y is the main sequence

%o def sequence():

%o     a = 1

%o     y.append(a)

%o     for i in range(num):

%o         if (a != 1) and (math.gcd(a,i+1) == 1):

%o             a -= 1

%o         else:

%o             a += math.gcd(a,i+1)+1

%o         x.append(i)

%o         y.append(a)

%o     x.append(num)

%o sequence()

%o # code only regarding the plot.

%o plt.xlim(0,num)

%o plt.ylim(0,num)

%o plt.plot(x, y)

%o plt.xlabel('x - axis')

%o plt.ylabel('y - axis')

%o plt.title('Plot of Sequence')

%o plt.show()

%K nonn,look

%O 0,2

%A _Nathaniel J. Strout_, Feb 24 2020