A374612 a(n) = n for n <= 3; 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 is also coprime to a(n-1).

1, 2, 3, 4, 9, 8, 15, 14, 5, 6, 25, 7, 10, 21, 16, 27, 20, 33, 26, 11, 12, 35, 13, 18, 49, 22, 39, 28, 45, 32, 51, 38, 17, 19, 24, 55, 34, 57, 40, 63, 44, 65, 36, 77, 30, 91, 46, 75, 23, 42, 85, 48, 95, 52, 69, 50, 81, 56, 87, 62, 29, 31, 54, 115, 58, 93, 64, 99, 68, 105, 74, 117, 37, 60, 119, 66

Offset: 1

Author

Scott R. Shannon, Jul 14 2024

Keywords

• nonn

Comments

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, and the fixed points are 1, 2, 3, 4, 28, 98; it is likely no more exist. The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(11) = 25 as 25 is coprime to a(10) = 6 while sharing a factor with a(9) = 5, which is itself coprime to a(10) = 6. Note that all other previous terms, other than a(1) = 1, do share a factor with a(10) = 6. This is the first term to differ from A373390.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A373390, A089088, A373998, A098550, A247942.