A359535 Lexicographically earliest sequence of distinct positive integers such that a(a(n)) and a(a(n+1)) share a common factor when n >= 2.

1, 2, 4, 6, 3, 8, 5, 12, 7, 10, 13, 15, 14, 16, 18, 20, 9, 22, 11, 28, 17, 91, 19, 25, 33, 21, 29, 39, 34, 23, 32, 38, 51, 57, 24, 37, 40, 26, 42, 30, 43, 69, 46, 27, 47, 58, 87, 31, 35, 44, 52, 54, 36, 74, 41, 59, 50, 60, 86, 48, 62, 93, 45, 65, 94, 49, 63, 53, 70, 72, 55, 82, 56, 1591

Offset: 1

Author

Neal Gersh Tolunsky, Jan 04 2023

Keywords

• nonn

Comments

The common factor rule does not apply at n=1 so the sequence starts with a(1) = 1 and a(2) = 2.

Examples

			a(3) cannot be 3 since then a(a(2))=2 and a(a(3))=3 would have no common factor, but a(3) = 4 is allowed (and puts a constraint on the subsequent a(4) value).
a(6) is 8 because so far we have (1,2,4,6,3). We see that the 6th term must share a factor with the 4th and 3rd terms, which are 6 and 4, respectively. The smallest number not already used that satisfies this property is 8.
		

Links

• Samuel Harkness, Table of n, a(n) for n = 1..10000
• Samuel Harkness, MATLAB program

Crossrefs

Cf. A064413.

Programs

MATLAB

See Links section.