OFFSET
1,2
COMMENTS
The sequence can always be extended with a multiple of 36; after a multiple of 36, we can extend the sequence with the least unused number; as there are infinitely many multiples of 36, this sequence is a permutation of the natural numbers (with inverse A285576).
For any k>=0, let c_k be the lexicographically earliest sequence of distinct terms such that the product of two consecutive terms is divisible by p^2 for at least k distinct primes p; in particular we have:
- c_0 = A000027 (the natural numbers),
- c_1 = A285296,
- c_2 = a (this sequence).
For any k>=0, c_k is a permutation of the natural numbers.
LINKS
EXAMPLE
The first terms, alongside the primes p such that p^2 divides a(n)*a(n+1), are:
n a(n) p
-- ---- ----
1 1 2, 3
2 36 2, 3
3 2 2, 3
4 18 2, 3
5 4 2, 3
6 9 2, 3
7 8 2, 5
8 25 2, 5
9 12 2, 3
10 3 2, 3
11 24 2, 3
12 6 2, 3
13 30 2, 5
14 10 2, 5
15 20 2, 5
16 5 2, 5
17 40 2, 5
18 15 3, 5
19 45 2, 3
20 16 2, 3
...
115 160 2, 5
116 115 2, 3, 5
117 180 2, 3
...
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Apr 22 2017
STATUS
approved