cp's OEIS Frontend

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).

%I A288923 #14 Jan 21 2018 09:38:33
%S A288923 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,
%T A288923 60,21,72,5,80,7,96,11,108,13,112,17,120,19,128,22,81,25,84,26,88,33,
%U A288923 90,34,100,35,104,38,126,39,132,42,44,45,50,52,63,66,68,70
%N 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).
%C A288923 The number of prime factors counted with multiplicity is given by A001222.
%C A288923 This sequence is a permutation of the natural numbers, with inverse A288924.
%C A288923 Conjecturally, a(n) ~ n.
%C A288923 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:
%C A288923 - f(bigomega,  6) = a (this sequence), where bigomega = A001222,
%C A288923 - f(tau,      34) = A288921,           where tau = A000005,
%C A288923 - f(omega,     5) = A285487,           where omega = A001221,
%C A288923 - f(omega,     6) = A285655,           where omega = A001221.
%C A288923 Some of these sequences have similar graphical features.
%H A288923 Rémy Sigrist, <a href="/A288923/b288923.txt">Table of n, a(n) for n = 1..20000</a>
%H A288923 Rémy Sigrist, <a href="/A288923/a288923.gp.txt">PARI program for A288923</a>
%H A288923 Rémy Sigrist, <a href="/A288923/a288923.png">Colored scatterplot of a(n) for n = 1..20000</a> (where the color is function of A001222(a(n)))
%H A288923 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A288923 The first terms, alongside a(n) * a(n+1) and its number of prime divisors counted with multiplicity, are:
%e A288923    n   a(n)   a(n)*a(n+1)   Bigomega
%e A288923   --   ----   -----------   --------
%e A288923    1     1         64           6
%e A288923    2    64        128           7
%e A288923    3     2         64           6
%e A288923    4    32         96           6
%e A288923    5     3        144           6
%e A288923    6    48        192           7
%e A288923    7     4         64           6
%e A288923    8    16         96           6
%e A288923    9     6        144           6
%e A288923   10    24        192           7
%e A288923   11     8         96           6
%e A288923   12    12        216           6
%e A288923   13    18        360           6
%e A288923   14    20        540           6
%e A288923   15    27        756           6
%e A288923   16    28        840           6
%e A288923   17    30       1080           7
%e A288923   18    36        324           6
%e A288923   19     9        360           6
%e A288923   20    40        400           6
%Y A288923 Cf. A001221, A001222, A285487, A285655, A288921, A288924 (inverse).
%K A288923 nonn,look
%O A288923 1,2
%A A288923 _Rémy Sigrist_, Jun 19 2017