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