OFFSET
1,1
COMMENTS
In other words, a(1), a(2), a(1)*a(2), a(3), a(4), a(3)*a(4), a(1)*a(2)*a(3)*a(4), a(5), a(6), a(5)*a(6), etc. are all distinct.
In particular, all terms are distinct (but not necessarily in increasing order).
We can arrange the terms of the sequence as the leaves of a perfect infinite binary tree, the products with e > 0 corresponding to parent nodes; each node will contain a different value and all values will appear in the tree (if n = 2^m+1 for some m > 0, then a(n) will equal the least value > 1 missing so far in the tree).
This sequence is a variant of A361144 where we use products instead of sums.
LINKS
Rémy Sigrist, PARI program
EXAMPLE
The first terms (at the bottom of the tree) alongside the corresponding products are:
1067062284288000
---------------------------------
604800 1764322560
----------------- -----------------
120 5040 24024 73440
--------- --------- --------- ---------
6 20 56 90 132 182 240 306
----- ----- ----- ----- ----- ----- ----- -----
2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 03 2023
STATUS
approved