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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
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, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76
OFFSET
1,1
COMMENTS
By necessity, all terms are distinct and strictly greater than 1.
This sequence is a variant of A101274.
Does every positive integer correspond to a product of consecutive terms?
FORMULA
a(n) = A079854(n+2) / A079854(n+1).
EXAMPLE
The values of a(i) * ... * a(j) for i <= j <= 7 are:
i\j| 1 2 3 4 5 6 7
---+---------------------------------
1| 2 6 24 120 840 6720 60480
2| . 3 12 60 420 3360 30240
3| . . 4 20 140 1120 10080
4| . . . 5 35 280 2520
5| . . . . 7 56 504
6| . . . . . 8 72
7| . . . . . . 9
PROG
(PARI) See Links section.
CROSSREFS
Cf. A079854, A101274 (additive variant), A333555 (XOR variant).
Sequence in context: A049093 A098901 A098767 * A153381 A307750 A356734
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 26 2020
STATUS
approved