cp's OEIS Frontend

A375563 a(1) = 1; for n > 1, a(n) is the smallest unused positive number that shares a factor with a(n-1) if a(n-1) is prime, otherwise a(n) is coprime to a(n-1).

%I A375563 #11 Sep 20 2024 06:37:40
%S A375563 1,2,4,3,6,5,10,7,14,9,8,11,22,13,26,15,16,17,34,19,38,21,20,23,46,25,
%T A375563 12,29,58,27,28,31,62,33,32,35,18,37,74,39,40,41,82,43,86,45,44,47,94,
%U A375563 49,24,53,106,51,50,57,52,55,36,59,118,61,122,63,64,65,42,67,134,69,56,71,142,73,146
%N A375563 a(1) = 1; for n > 1, a(n) is the smallest unused positive number that shares a factor with a(n-1) if a(n-1) is prime, otherwise a(n) is coprime to a(n-1).
%C A375563 The terms are all concentrated along three lines with the central line, consisting entirely of all the odd terms, along the line a(n) = n. Surprisingly however there are no fixed points in the first 100000 terms. In the same range the primes appear in their natural order. The sequence is conjectured to be a permutation of the positive integers.
%H A375563 Scott R. Shannon, <a href="/A375563/b375563.txt">Table of n, a(n) for n = 1..10000</a>
%e A375563 a(6) = 5 as a(5) = 6 is a composite number, and 5 is the smallest unused number that is coprime to 6.
%Y A375563 Cf. A375564, A064413, A000040, A373546, A373545.
%K A375563 nonn
%O A375563 1,2
%A A375563 _Scott R. Shannon_, Aug 19 2024