A348386 Lexicographically earliest sequence of positive integers such that for any n > 0, a(n) is the number of nonempty runs of consecutive terms whose sum is n.

1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 22, 22

Offset

1,2

Comments

This sequence has similarities with Golomb's sequence (A001462); here we consider sums of one or more consecutive terms, there single terms.

This sequence is not weakly increasing: a(724) = 91 > a(725) = 90.

Links

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

Rémy Sigrist, C program for A348386

Example

The first terms, alongside the sums a(n), a(n)+a(n-1), ..., are:
  n   a(n)  Partial sums
  --  ----  -------------------------------------
   1     1  1
   2     2  2, 3
   3     2  2, 4, 5
   4     3  3, 5, 7, 8
   5     4  4, 7, 9, 11, 12
   6     4  4, 8, 11, 13, 15, 16
   7     5  5, 9, 13, 16, 18, 20, 21
   8     5  5, 10, 14, 18, 21, 23, 25, 26
   9     6  6, 11, 16, 20, 24, 27, 29, 31, 32
  10     6  6, 12, 17, 22, 26, 30, 33, 35, 37, 38

Prog

(C) See Links section.

Crossrefs

Cf. A001462, A348385 (multiplicative variant).

Sequence in context: A089575 A227737 A194177 * A023190 A047783 A321667

Adjacent sequences: A348383 A348384 A348385 * A348387 A348388 A348389

Keyword

nonn

Author

Rémy Sigrist, Oct 16 2021

Status

approved