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A285487 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 5 distinct prime factors.

%I A285487 #18 Jun 14 2017 02:47:06
%S A285487 1,2310,2,1155,4,1365,6,385,12,455,18,595,22,105,26,165,14,195,28,255,
%T A285487 38,210,11,390,7,330,13,420,17,462,5,546,10,231,20,273,30,77,60,91,66,
%U A285487 35,78,55,42,65,84,85,114,70,33,130,21,110,39,140,51,154,15,182
%N A285487 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 5 distinct prime factors.
%C A285487 This sequence can always be extended with a multiple of 2310 = 2*3*5*7*11; after a term that has at least 5 distinct prime factors, we can extend the sequence with the least unused number; as there are infinitely many numbers with at least 5 distinct prime factors, this sequence is a permutation of the natural numbers (with inverse A285488).
%C A285487 Conjecturally, a(n) ~ n.
%C A285487 The first fixed points are: 1, 75, 295, 375, 1205, 1207, 1211, 6017, 19870, 19872, 19874, 19878, 19907, 19909.
%H A285487 Rémy Sigrist, <a href="/A285487/b285487.txt">Table of n, a(n) for n = 1..30000</a>
%H A285487 Rémy Sigrist, <a href="/A285487/a285487.txt">C++ program for A285487</a>
%H A285487 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A285487 The first terms, alongside the primes p dividing a(n)*a(n+1), are:
%e A285487 n       a(n)    p
%e A285487 --      ----    --------------
%e A285487 1       1       2, 3, 5, 7, 11
%e A285487 2       2310    2, 3, 5, 7, 11
%e A285487 3       2       2, 3, 5, 7, 11
%e A285487 4       1155    2, 3, 5, 7, 11
%e A285487 5       4       2, 3, 5, 7,     13
%e A285487 6       1365    2, 3, 5, 7,     13
%e A285487 7       6       2, 3, 5, 7, 11
%e A285487 8       385     2, 3, 5, 7, 11
%e A285487 9       12      2, 3, 5, 7,     13
%e A285487 10      455     2, 3, 5, 7,     13
%e A285487 11      18      2, 3, 5, 7,        17
%e A285487 12      595     2,    5, 7, 11,    17
%e A285487 13      22      2, 3, 5, 7, 11
%e A285487 14      105     2, 3, 5, 7, 13
%e A285487 15      26      2, 3, 5,    11, 13
%e A285487 16      165     2, 3, 5, 7, 11
%e A285487 17      14      2, 3, 5, 7,     13
%e A285487 18      195     2, 3, 5, 7,     13
%e A285487 19      28      2, 3, 5, 7,        17
%e A285487 20      255     2, 3, 5,           17, 19
%Y A285487 Cf. A285488.
%K A285487 nonn,look
%O A285487 1,2
%A A285487 _Rémy Sigrist_, Apr 19 2017