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A348385
Lexicographically earliest sequence of positive integers such that for any n > 0, a(n) is the number of nonempty runs of consecutive terms whose product is n.
2
1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17
OFFSET
1,2
COMMENTS
This sequence has similarities with Golomb's sequence (A001462); here we consider products of one or more consecutive terms, there single terms.
This sequence is weakly increasing.
EXAMPLE
The first terms, alongside the products a(n), a(n)*a(n-1), ..., are:
n a(n) Partial products
-- ---- -------------------------------------------------------
1 1 1
2 2 2, 2
3 3 3, 6, 6
4 3 3, 9, 18, 18
5 3 3, 9, 27, 54, 54
6 4 4, 12, 36, 108, 216, 216
7 4 4, 16, 48, 144, 432, 864, 864
8 4 4, 16, 64, 192, 576, 1728, 3456, 3456
9 5 5, 20, 80, 320, 960, 2880, 8640, 17280, 17280
10 5 5, 25, 100, 400, 1600, 4800, 14400, 43200, 86400, 86400
PROG
(C) See Links section.
CROSSREFS
Cf. A001462, A348386 (additive variant).
Sequence in context: A196176 A121536 A285761 * A080405 A039728 A332965
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Oct 16 2021
STATUS
approved