cp's OEIS Frontend

A374645 a(1) = 1, a(2) = 6, a(3) = 2; for n > 3, a(n) is the smallest unused positive number that is coprime to a(n-1) but has a common factor with any other previous term that has a common factor with a(n-1).

%I A374645 #10 Jul 16 2024 08:08:52
%S A374645 1,6,2,3,4,9,8,15,14,27,5,12,7,10,21,16,25,18,35,22,39,20,11,24,13,30,
%T A374645 49,26,33,28,45,32,51,38,55,34,19,36,17,40,57,44,63,46,65,42,23,48,77,
%U A374645 50,69,52,75,56,81,58,85,54,29,60,91,62,87,64,31,66,95,68,93,70,99,74,105,76,37
%N A374645 a(1) = 1, a(2) = 6, a(3) = 2; for n > 3, a(n) is the smallest unused positive number that is coprime to a(n-1) but has a common factor with any other previous term that has a common factor with a(n-1).
%C A374645 The terms appear to follow a pattern similar to the A064413 and A373390, i.e., the terms are concentrated along just three lines of different gradient, and the lower line consists only of primes. In the first 10000 terms the primes appear in their natural order except for a(37) = 19 and a(39) = 17 which are reversed. Many fixed points exist, 2228 in the first 10000 terms, these beginning 1, 12, 16, 18, 24, 32, 40, 48, ... . The sequence is conjectured to be a permutation of the positive integers.
%H A374645 Scott R. Shannon, <a href="/A374645/b374645.txt">Table of n, a(n) for n = 1..10000</a>
%e A374645 a(11) = 5 as 5 is coprime to a(10) = 27 while sharing a factor with a(8) = 15, which itself shares a factor with a(10) = 27. This is also the first term that uses a term other than a(2) = 6 as the previous term with which is shares a factor with.
%Y A374645 Cf. A374612, A373390, A089088, A373998, A098550, A247942.
%K A374645 nonn
%O A374645 1,2
%A A374645 _Scott R. Shannon_, Jul 15 2024