OFFSET
1,3
COMMENTS
See A317025 for the corresponding LCM.
This sequence has similarities with A088177.
For any n > 0, let g(n) = gcd(a(n), a(n+1)); between 1 and 800000, the function g takes only 5 times a value other than 1.
For any n > 0 and prime number p, if p divides a(n+1), then the p-adic valuation of a(n+1) is strictly greater than the p-adic valuation of a(n).
This sequence contains infinitely many distinct values.
The first occurrence of a prime number p, if not preceded by 1, is followed by 1.
The first occurrence of a prime power k, if not preceded by a divisor of k, is followed by 1.
If this sequence contains infinitely many 1's, then A317025 is a permutation of the natural numbers.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A317024
EXAMPLE
The first terms, alongside lcm(a(n), a(n+1)), are:
n a(n) lcm(a(n), a(n+1))
-- ---- -----------------
1 1 1
2 1 2
3 2 6
4 3 3
5 1 4
6 4 12
7 3 15
8 5 5
9 1 7
10 7 14
11 2 10
12 5 20
13 4 28
14 7 21
15 3 24
16 8 8
17 1 9
18 9 18
19 2 22
20 11 11
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 19 2018
STATUS
approved