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A327439 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.

%I A327439 #27 Dec 17 2024 22:54:15
%S A327439 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 A327439 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 A327439 19,18,17,16,15,14,13,12,11
%N A327439 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 A327439 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 A327439 See Python program for zoomable graph.
%H A327439 Nathaniel J. Strout, <a href="/A327439/b327439.txt">Table of n, a(n) for n = 0..116000</a>
%t A327439 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 A327439 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 A327439 (Python)
%o A327439 import math
%o A327439 import matplotlib.pyplot as plt
%o A327439 num = 10000
%o A327439 x = []
%o A327439 y = []
%o A327439 # y is the main sequence
%o A327439 def sequence():
%o A327439     a = 1
%o A327439     y.append(a)
%o A327439     for i in range(num):
%o A327439         if (a != 1) and (math.gcd(a,i+1) == 1):
%o A327439             a -= 1
%o A327439         else:
%o A327439             a += math.gcd(a,i+1)+1
%o A327439         x.append(i)
%o A327439         y.append(a)
%o A327439     x.append(num)
%o A327439 sequence()
%o A327439 # code only regarding the plot.
%o A327439 plt.xlim(0,num)
%o A327439 plt.ylim(0,num)
%o A327439 plt.plot(x, y)
%o A327439 plt.xlabel('x - axis')
%o A327439 plt.ylabel('y - axis')
%o A327439 plt.title('Plot of Sequence')
%o A327439 plt.show()
%K A327439 nonn,look
%O A327439 0,2
%A A327439 _Nathaniel J. Strout_, Feb 24 2020