A387231 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) if a(n-1) > a(n-2), else it is coprime to a(n-1) if a(n-1) < a(n-2).

1, 2, 4, 6, 3, 5, 10, 8, 7, 9, 12, 14, 16, 18, 15, 11, 13, 26, 20, 17, 19, 38, 22, 21, 23, 46, 24, 25, 30, 27, 28, 32, 34, 36, 33, 29, 31, 62, 40, 37, 35, 39, 42, 44, 48, 45, 41, 43, 86, 50, 47, 49, 56, 52, 51, 53, 106, 54, 55, 60, 57, 58, 64, 66, 63, 59, 61

Offset

1,2

Comments

The sequence is composed of two main lines of terms, the upper being even semiprimes, while the lower contains all other terms. For the terms studied the primes appear in their natural order.

In the first 100000 terms the fixed points are 1, 2, 8, 15, 32, 44, 50, 60, 90, 182, 198, 220; it is likely no more exist. 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(4) = 6 as a(3) = 4 > a(2) = 3, and 6 is the smallest unused number that shares a factor with 4.
a(6) = 5 as a(5) = 3 < a(4) = 6, and 5 is the smallest unused number that is coprime to 3.

Crossrefs

Cf. A387757, A384045, A375563, A375564, A373545, A064413.

Sequence in context: A369293 A104492 A331522 * A075075 A088178 A259840

Adjacent sequences: A387228 A387229 A387230 * A387232 A387233 A387234

Keyword

nonn

Author

Scott R. Shannon, Aug 23 2025

Status

approved