OFFSET
1,2
COMMENTS
In other words, consecutive terms differ exactly by one prime factor.
This sequence has strong connections with A163252:
- here consecutive terms differ by one prime factor, there by one binary digit,
- for any n > 0, A163252(n-1) encodes in binary form the prime numbers appearing in a(n).
Odd indexed terms have an even number of prime factors and vice versa.
For any prime number p: as there are only finitely many squarefree numbers with greatest prime factor < p, eventually the sequence contains a multiple of p.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A330919
EXAMPLE
The first terms, alongside their prime factors, are:
n a(n) prime factors
-- ---- -------------
1 1
2 2 2
3 6 2, 3
4 3 3
5 15 3, 5
6 5 5
7 10 2, 5
8 30 2, 3, 5
9 210 2, 3, 5, 7
10 42 2, 3, 7
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, May 02 2020
STATUS
approved