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).

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, 49, 26, 33, 28, 45, 32, 51, 38, 55, 34, 19, 36, 17, 40, 57, 44, 63, 46, 65, 42, 23, 48, 77, 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

Offset

1,2

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 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.

Links

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

Example

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.

Crossrefs

Cf. A374612, A373390, A089088, A373998, A098550, A247942.

Sequence in context: A362922 A019662 A330531 * A134105 A167509 A011362

Adjacent sequences: A374642 A374643 A374644 * A374646 A374647 A374648

Keyword

nonn

Author

Scott R. Shannon, Jul 15 2024

Status

approved