A375563 a(1) = 1; for n > 1, a(n) is the smallest unused positive number that shares a factor with a(n-1) if a(n-1) is prime, otherwise a(n) is coprime to a(n-1).

1, 2, 4, 3, 6, 5, 10, 7, 14, 9, 8, 11, 22, 13, 26, 15, 16, 17, 34, 19, 38, 21, 20, 23, 46, 25, 12, 29, 58, 27, 28, 31, 62, 33, 32, 35, 18, 37, 74, 39, 40, 41, 82, 43, 86, 45, 44, 47, 94, 49, 24, 53, 106, 51, 50, 57, 52, 55, 36, 59, 118, 61, 122, 63, 64, 65, 42, 67, 134, 69, 56, 71, 142, 73, 146

Offset: 1

Author

Scott R. Shannon, Aug 19 2024

Keywords

• nonn

Comments

The terms are all concentrated along three lines with the central line, consisting entirely of all the odd terms, along the line a(n) = n. Surprisingly however there are no fixed points in the first 100000 terms. In the same range the primes appear in their natural order. The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(6) = 5 as a(5) = 6 is a composite number, and 5 is the smallest unused number that is coprime to 6.
		

Links

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

Crossrefs

Cf. A375564, A064413, A000040, A373546, A373545.