A338292 Lexicographically earliest sequence of positive integers such that for any distinct m and n, (a(m+1-a(m)), ..., a(m)) <> (a(n+1-a(n)), ..., a(n)).

1, 2, 2, 3, 2, 3, 3, 3, 4, 2, 3, 4, 3, 3, 4, 4, 3, 4, 4, 4, 4, 5, 2, 3, 4, 4, 5, 3, 3, 4, 5, 4, 3, 4, 5, 5, 3, 4, 4, 5, 4, 4, 4, 5, 5, 4, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 5, 6, 2, 3, 4, 5, 5, 5, 6, 3, 3, 4, 5, 5, 6, 4, 3, 4, 5, 6, 4, 4, 4, 5, 6, 5, 3, 4, 5, 5

Offset

1,2

Comments

In other words, for any n > 0, the tuple comprising the a(n) terms up to and including a(n) is always unique.

This sequence is unbounded.

The number 1 appears once.

The number 2 appears after the first occurrence of a number.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A338292

Example

The first terms, alongside the corresponding tuples, are:
  n   a(n)  (a(n+1-a(n)), ..., a(n))
  --  ----  ------------------------
   1     1  (1)
   2     2  (1, 2)
   3     2     (2, 2)
   4     3     (2, 2, 3)
   5     2           (3, 2)
   6     3           (3, 2, 3)
   7     3              (2, 3, 3)
   8     3                 (3, 3, 3)
   9     4                 (3, 3, 3, 4)
  10     2                          (4, 2)
  11     3                          (4, 2, 3)
  12     4                          (4, 2, 3, 4)
  13     3                                (3, 4, 3)
  14     3                                   (4, 3, 3)
  15     4                                   (4, 3, 3, 4)
  16     4                                      (3, 3, 4, 4)

Prog

(PARI) See Links section.

Crossrefs

See A338283 for a similar sequence.

Sequence in context: A057941 A358550 A126071 * A359728 A217865 A185166

Adjacent sequences: A338289 A338290 A338291 * A338293 A338294 A338295

Keyword

nonn

Author

Rémy Sigrist, Oct 20 2020

Status

approved