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A365060 a(1) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has a common factor with A008472(a(n-1)), the sum of the distinct primes dividing a(n-1).

%I A365060 #8 Sep 18 2023 09:01:29
%S A365060 2,4,6,5,10,7,14,3,9,12,15,8,16,18,20,21,22,13,26,24,25,30,28,27,33,
%T A365060 32,34,19,38,35,36,40,42,39,44,52,45,46,50,49,56,48,55,54,60,58,31,62,
%U A365060 11,66,64,68,57,70,63,65,51,72,75,74,69,76,77,78,80,84,81,87,82,43,86,85,88,91,90,92,95
%N A365060 a(1) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has a common factor with A008472(a(n-1)), the sum of the distinct primes dividing a(n-1).
%C A365060 In the first 100000 terms the only fixed point is 9, and it is likely no more exist. In the same range the smallest missing numbers are 503, 839, 877. The sequence is conjectured to be a permutation of the integers >= 2.
%H A365060 Scott R. Shannon, <a href="/A365060/b365060.txt">Table of n, a(n) for n = 1..10000</a>.
%H A365060 Scott R. Shannon, <a href="/A365060/a365060.png">Image of the first 100000 terms</a>. The green line is a(n) = n.
%e A365060 a(3) = 6 as a(2) = 4 and A008472(4) = 2, and 6 is the smallest unused number that shares a factor with 2.
%e A365060 a(8) = 3 as a(7) = 14 and A008472(14) = 9, and 3 is the smallest unused number that shares a factor with 9.
%Y A365060 Cf. A008472, A365059, A300813.
%K A365060 nonn
%O A365060 1,1
%A A365060 _Scott R. Shannon_, Aug 19 2023