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A333559 Lexicographically earliest infinite sequence of positive terms such that for any two distinct nonempty intervals, say [t, u] and [v, w], a(t) * ... * a(u) <> a(v) * ... * a(w).

%I A333559 #9 Mar 30 2020 08:45:34
%S A333559 2,3,4,5,7,8,9,10,11,13,14,15,17,16,18,19,21,22,23,25,26,27,28,29,30,
%T A333559 31,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
%U A333559 55,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76
%N A333559 Lexicographically earliest infinite sequence of positive terms such that for any two distinct nonempty intervals, say [t, u] and [v, w], a(t) * ... * a(u) <> a(v) * ... * a(w).
%C A333559 By necessity, all terms are distinct and strictly greater than 1.
%C A333559 This sequence is a variant of A101274.
%C A333559 Does every positive integer correspond to a product of consecutive terms?
%H A333559 Rémy Sigrist, <a href="/A333559/a333559.gp.txt">PARI program for A333559</a>
%F A333559 a(n) = A079854(n+2) / A079854(n+1).
%e A333559 The values of a(i) * ... * a(j) for i <= j <= 7 are:
%e A333559   i\j|  1  2   3    4    5     6      7
%e A333559   ---+---------------------------------
%e A333559     1|  2  6  24  120  840  6720  60480
%e A333559     2|  .  3  12   60  420  3360  30240
%e A333559     3|  .  .   4   20  140  1120  10080
%e A333559     4|  .  .   .    5   35   280   2520
%e A333559     5|  .  .   .    .    7    56    504
%e A333559     6|  .  .   .    .    .     8     72
%e A333559     7|  .  .   .    .    .     .      9
%o A333559 (PARI) See Links section.
%Y A333559 Cf. A079854, A101274 (additive variant), A333555 (XOR variant).
%K A333559 nonn
%O A333559 1,1
%A A333559 _Rémy Sigrist_, Mar 26 2020