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.

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.

Links

Table of n, a(n) for n=1..71.

Rémy Sigrist, C program for A348385

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

Adjacent sequences: A348382 A348383 A348384 * A348386 A348387 A348388

Keyword

nonn

Author

Rémy Sigrist, Oct 16 2021

Status

approved