OFFSET
1,2
COMMENTS
a(A100112(n)) and A100114(A100112(n)) define a pair of inverse permutations of the squarefree numbers: a(A100112(A100114(n))) = A100114(A100112(a(n))) = A005117(n);
Comments from N. J. A. Sloane, Oct 29 2020 (Start)
An alternative definition is that this is the lexicographically earliest infinite sequence of distinct positive squarefree numbers with the property that gcd(a(n), a(n-1)) > 1 for n >= 3.
Described in this way, this is a squarefree version of the EKG sequence A064413, and it is easy to modify the proof that that sequence is a permutation of the positive integers so as to show that the present sequence is a permutation of the positive squarefree numbers, as claimed in the first comment.
Conjecture: With the three exceptions p = 2, 5, 13, and 31, when a prime p appears it is preceded by 2*p and followed by 3*p.
(End)
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Squarefree
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 07 2004
STATUS
approved