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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. 2
 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)
 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. LINKS 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 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. Cf. A000010, A057979, A088177. Sequence in context: A075850 A327565 A054437 * A287821 A341830 A357714 Adjacent sequences: A335940 A335941 A335942 * A335944 A335945 A335946 KEYWORD nonn AUTHOR Rémy Sigrist, Jul 01 2020 STATUS approved

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Last modified January 28 18:26 EST 2023. Contains 359905 sequences. (Running on oeis4.)