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A335943
Lexicographically earliest sequence of positive terms such that for any distinct m and n, the fractional parts of a(m)/a(m+1) and of a(n)/a(n+1) are distinct.
3
1, 1, 2, 3, 4, 3, 5, 4, 5, 6, 5, 7, 5, 8, 7, 6, 7, 8, 9, 7, 9, 8, 11, 7, 10, 7, 11, 8, 13, 9, 10, 9, 11, 9, 13, 10, 11, 10, 13, 11, 12, 11, 13, 12, 13, 14, 9, 14, 11, 14, 13, 15, 11, 15, 13, 16, 11, 16, 13, 17, 11, 17, 12, 17, 13, 18, 13, 19, 12, 19, 13, 20
OFFSET
1,3
COMMENTS
For any k > 1, k appears up to A000010(k) times.
This sequence has similarities with A057979 and A088177, where we consider the ratio and the product of consecutive terms, respectively.
EXAMPLE
The first terms, alongside the fractional part of a(n)/a(n+1), are:
n a(n) frac(a(n)/a(n+1))
-- ---- -----------------
1 1 0
2 1 1/2
3 2 2/3
4 3 3/4
5 4 1/3
6 3 3/5
7 5 1/4
8 4 4/5
9 5 5/6
10 6 1/5
PROG
(PARI) See Links section.
CROSSREFS
See A335944 for a similar sequence.
Sequence in context: A075850 A327565 A054437 * A287821 A341830 A357714
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 01 2020
STATUS
approved