cp's OEIS Frontend

A349492 a(1)=1, a(2)=6; for n > 2, a(n) is the smallest unused positive number such that gcd(a(n-1)+n, a(n)) > 1, gcd(a(n-1), a(n)) > 1, and gcd(n, a(n)) > 1.

%I A349492 #14 Nov 20 2021 20:22:30
%S A349492 1,6,3,42,470,2,84,4,78,8,418,10,598,12,9,30,1598,14,114,16,222,18,
%T A349492 1886,20,5,310,2022,22,174,15,186,24,21,60,25,610,47878,26,13,1378,
%U A349492 246,27,258,28,438,32,7426,34,1162,36,33,90,1166,38,66,40,582,44,12154,46,13054,48,39,618,6830
%N A349492 a(1)=1, a(2)=6; for n > 2, a(n) is the smallest unused positive number such that gcd(a(n-1)+n, a(n)) > 1, gcd(a(n-1), a(n)) > 1, and gcd(n, a(n)) > 1.
%C A349492 The majority of terms lie near a line of gradient 1, but some terms show extremely large jumps in value, e.g., in the first 30000 terms the largest value is a(25391) = 87893333254. It is likely all numbers eventually appear although this is unknown. In the same range, and other than a(3) = 3, there are twenty-one fixed points all between 626 to 856 inclusive. As the terms for n>30000 appear both above and below the line y = n it is possible more exist although this is unknown.
%H A349492 Scott R. Shannon, <a href="/A349492/a349492.png">Image for the first 10000 points with values below 20000</a>. The green line is y = n.
%H A349492 Scott R. Shannon, <a href="/A349492/a349492_1.png">Image of the first 30000 terms</a>. On this scale the vast majority of terms lie along the x-axis.
%e A349492 a(3) = 3 as a(2)+3 = 9, gcd(9,3)>1, gcd(6,3)>1, gcd(3,3)>1 and 3 has not been used.
%e A349492 a(4) = 42 as a(3)+4 = 7, gcd(7,42)>1, gcd(3,42)>1, gcd(4,42)>1 and 42 has not been used.
%e A349492 a(5) = 470 as a(4)+5 = 47, gcd(47,470)>1, gcd(42,470)>1, gcd(5,470)>1 and 470 has not been used.
%e A349492 a(6) = 2 as a(5)+6 = 476, gcd(476,2)>1, gcd(470,2)>1, gcd(6,2)>1 and 2 has not been used.
%t A349492 a[1]=1; a[2]=6; a[n_]:=a[n]=(k=2;While[MemberQ[Array[a,n-1],k]||GCD[a[n-1]+n,k]<=1||GCD[a[n-1],k]<=1||GCD[n,k]<=1,k++];k); Array[a,65] (* _Giorgos Kalogeropoulos_, Nov 20 2021 *)
%o A349492 (Python)
%o A349492 from math import gcd
%o A349492 terms, appears = [1, 6], {6:True}
%o A349492 for n in range(3, 100):
%o A349492     t = 2
%o A349492     while not (appears.get(t) is None and gcd(terms[-1]+n, t)>1 and gcd(terms[-1], t)>1 and gcd(n, t)>1):
%o A349492         t += 1
%o A349492     appears[t] = True; terms.append(t)
%o A349492 print(terms) # _Gleb Ivanov_, Nov 20 2021
%Y A349492 Cf. A119018, A064413, A349472.
%K A349492 nonn
%O A349492 1,2
%A A349492 _Scott R. Shannon_, Nov 19 2021