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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)))

Index entries for sequences that are permutations of the natural numbers

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.)