16 Aug
2020
16 Aug
'20
9:18 a.m.
On 16/08/2020 04:54, Neil Sloane wrote:
Definition: Lexicographically earliest sequence {a(n)} of distinct positive numbers such that, for n>2, a(n) has a common factor with a(n-1) but not with a(n-2). 1, 2, 6, 15, 35, 14, 12, 33, 55, 10, 18, 21, 77, 22, 20, 45, 39, 26, 28, 63, ... The original idea was due to Scott, with a different sequence, but this is my (canonical!) version.
Could someone please prove the conjecture that this is a permutation of the set {1, all numbers with at least two distinct prime factors} ?
Nitpick: I can prove that it _isn't_ because 2 does not have at least two distinct prime factors. :-) I assume the correct fix is just to replace "1," with "1, 2,". -- g