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A317024
Lexicographically earliest sequence of positive terms such that for any distinct i and j, lcm(a(i), a(i+1)) and lcm(a(j), a(j+1)) are distinct.
3
1, 1, 2, 3, 1, 4, 3, 5, 1, 7, 2, 5, 4, 7, 3, 8, 1, 9, 2, 11, 1, 13, 2, 15, 4, 9, 5, 7, 6, 11, 3, 13, 4, 11, 5, 8, 7, 9, 8, 11, 7, 10, 9, 11, 10, 13, 5, 16, 1, 17, 2, 19, 1, 23, 2, 25, 1, 27, 2, 29, 1, 31, 2, 32, 3, 16, 7, 12, 11, 13, 6, 17, 3, 19, 4, 17, 5, 19
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.
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
Sequence in context: A161621 A095701 A067992 * A354803 A140757 A258254
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 19 2018
STATUS
approved