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