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A360305
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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.
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3
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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, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
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OFFSET
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1,1
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COMMENTS
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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.
In particular, all terms are distinct (but not necessarily in increasing order).
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).
This sequence is a variant of A361144 where we use products instead of sums.
The data section matches that of A249407, however a(115) = 121 whereas A249407(115) = 120.
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LINKS
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EXAMPLE
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The first terms (at the bottom of the tree) alongside the corresponding products are:
1067062284288000
---------------------------------
604800 1764322560
----------------- -----------------
120 5040 24024 73440
--------- --------- --------- ---------
6 20 56 90 132 182 240 306
----- ----- ----- ----- ----- ----- ----- -----
2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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