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%I #48 Mar 07 2023 07:42:23
%S 2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,
%T 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U 52,53,54,55,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71
%N Lexicographically earliest sequence of integers > 1 such that the products Product_{i = 1+k*2^e..(k+1)*2^e} a(i) with k, e >= 0 are all distinct.
%C In other words, a(1), a(2), a(1)*a(2), a(3), a(4), a(3)*a(4), a(1)*a(2)*a(3)*a(4), a(5), a(6), a(5)*a(6), etc. are all distinct.
%C In particular, all terms are distinct (but not necessarily in increasing order).
%C We can arrange the terms of the sequence as the leaves of a perfect infinite binary tree, the products with e > 0 corresponding to parent nodes; each node will contain a different value and all values will appear in the tree (if n = 2^m+1 for some m > 0, then a(n) will equal the least value > 1 missing so far in the tree).
%C This sequence is a variant of A361144 where we use products instead of sums.
%C The data section matches that of A249407, however a(115) = 121 whereas A249407(115) = 120.
%H Rémy Sigrist, <a href="/A360305/a360305.gp.txt">PARI program</a>
%e The first terms (at the bottom of the tree) alongside the corresponding products are:
%e 1067062284288000
%e ---------------------------------
%e 604800 1764322560
%e ----------------- -----------------
%e 120 5040 24024 73440
%e --------- --------- --------- ---------
%e 6 20 56 90 132 182 240 306
%e ----- ----- ----- ----- ----- ----- ----- -----
%e 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18
%o (PARI) See Links section.
%Y Cf. A249407, A361144, A361234.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 03 2023
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