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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). 1

%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

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Last modified September 26 23:47 EDT 2020. Contains 337378 sequences. (Running on oeis4.)