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).

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, 32, 34, 19, 38, 35, 36, 40, 42, 39, 44, 52, 45, 46, 50, 49, 56, 48, 55, 54, 60, 58, 31, 62, 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

Offset: 1

Author

Scott R. Shannon, Aug 19 2023

Keywords

• nonn

Comments

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.

Examples

			a(3) = 6 as a(2) = 4 and A008472(4) = 2, and 6 is the smallest unused number that shares a factor with 2.
a(8) = 3 as a(7) = 14 and A008472(14) = 9, and 3 is the smallest unused number that shares a factor with 9.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000.
• Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Crossrefs

Cf. A008472, A365059, A300813.