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 A288923 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 6 prime factors (counted with multiplicity). 3
 1, 64, 2, 32, 3, 48, 4, 16, 6, 24, 8, 12, 18, 20, 27, 28, 30, 36, 9, 40, 10, 54, 14, 56, 15, 60, 21, 72, 5, 80, 7, 96, 11, 108, 13, 112, 17, 120, 19, 128, 22, 81, 25, 84, 26, 88, 33, 90, 34, 100, 35, 104, 38, 126, 39, 132, 42, 44, 45, 50, 52, 63, 66, 68, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The number of prime factors counted with multiplicity is given by A001222. This sequence is a permutation of the natural numbers, with inverse A288924. Conjecturally, a(n) ~ n. For a function g over the natural numbers and a constant K, let f(g,K) be the lexicographically earliest sequence of distinct positive terms such that, for any n > 0, g( f(g,K)(n) * f(g,K)(n+1) ) >= K. In particular we have: - f(bigomega,  6) = a (this sequence), where bigomega = A001222, - f(tau,      34) = A288921,           where tau = A000005, - f(omega,     5) = A285487,           where omega = A001221, - f(omega,     6) = A285655,           where omega = A001221. Some of these sequences have similar graphical features. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..20000 Rémy Sigrist, PARI program for A288923 Rémy Sigrist, Colored scatterplot of a(n) for n = 1..20000 (where the color is function of A001222(a(n))) EXAMPLE The first terms, alongside a(n) * a(n+1) and its number of prime divisors counted with multiplicity, are:    n   a(n)   a(n)*a(n+1)   Bigomega   --   ----   -----------   --------    1     1         64           6    2    64        128           7    3     2         64           6    4    32         96           6    5     3        144           6    6    48        192           7    7     4         64           6    8    16         96           6    9     6        144           6   10    24        192           7   11     8         96           6   12    12        216           6   13    18        360           6   14    20        540           6   15    27        756           6   16    28        840           6   17    30       1080           7   18    36        324           6   19     9        360           6   20    40        400           6 CROSSREFS Cf. A001221, A001222, A285487, A285655, A288921, A288924 (inverse). Sequence in context: A303329 A301911 A302155 * A123964 A298923 A210114 Adjacent sequences:  A288920 A288921 A288922 * A288924 A288925 A288926 KEYWORD nonn,look AUTHOR Rémy Sigrist, Jun 19 2017 STATUS approved

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Last modified September 19 12:30 EDT 2020. Contains 337178 sequences. (Running on oeis4.)