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A335943
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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.
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2
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of (n, frac(a(n)/a(n+1))) for n = 1..50000
Rémy Sigrist, Colored scatterplot of (numerator(frac(a(n)/a(n+1))), denominator(frac(a(n)/a(n+1)))) for n = 1..232289 (where the hue is function of n)
Rémy Sigrist, PARI program for A335943
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EXAMPLE
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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
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A335944 for a similar sequence.
Cf. A000010, A057979, A088177.
Sequence in context: A075850 A327565 A054437 * A287821 A341830 A357714
Adjacent sequences: A335940 A335941 A335942 * A335944 A335945 A335946
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KEYWORD
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nonn
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AUTHOR
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Rémy Sigrist, Jul 01 2020
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STATUS
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approved
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