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%I #18 Jun 16 2017 22:22:03
%S 1,2,3,2310,1155,770,4,6,9,1365,385,910,8,12,11,1785,455,210,10,18,13,
%T 231,595,330,20,22,7,273,105,390,30,26,14,77,165,195,60,28,34,91,255,
%U 285,66,38,42,35,315,55,78,44,84,70,345,65,33,52,102,130,357,95
%N Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n)*a(n+3) has at least 5 distinct prime factors.
%C This sequence is a permutation of the natural numbers, with inverse A288800.
%C See also A288164 for similar sequences.
%C Conjecturally, a(n) ~ n.
%H Rémy Sigrist, <a href="/A288171/b288171.txt">Table of n, a(n) for n = 1..25000</a>
%H Rémy Sigrist, <a href="/A288171/a288171.txt">C++ program for A288171</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+3), are:
%e n a(n) p
%e -- ---- --------------
%e 1 1 2, 3, 5, 7, 11
%e 2 2 2, 3, 5, 7, 11
%e 3 3 2, 3, 5, 7, 11
%e 4 2310 2, 3, 5, 7, 11
%e 5 1155 2, 3, 5, 7, 11
%e 6 770 2, 3, 5, 7, 11
%e 7 4 2, 3, 5, 7, 13
%e 8 6 2, 3, 5, 7, 11
%e 9 9 2, 3, 5, 7, 13
%e 10 1365 2, 3, 5, 7, 13
%e 11 385 2, 3, 5, 7, 11
%e 12 910 2, 5, 7, 11, 13
%e 13 8 2, 3, 5, 7, 17
%e 14 12 2, 3, 5, 7, 13
%e 15 11 2, 3, 5, 7, 11
%e 16 1785 2, 3, 5, 7, 17
%e 17 455 2, 3, 5, 7, 13
%e 18 210 2, 3, 5, 7, 13
%e 19 10 2, 3, 5, 7, 11
%e 20 18 2, 3, 5, 7, 17
%Y Cf. A288164, A288800 (inverse).
%K nonn,look
%O 1,2
%A _Rémy Sigrist_, Jun 16 2017
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