A338283 Lexicographically earliest sequence of positive integers such that for any distinct m and n, Sum_{k = m+1-a(m)..m} a(k) <> Sum_{k = n+1-a(n)..n} a(k).

1, 2, 2, 3, 2, 3, 4, 2, 3, 4, 3, 4, 4, 3, 5, 4, 5, 4, 4, 5, 5, 6, 4, 5, 6, 5, 6, 5, 6, 6, 5, 7, 6, 6, 7, 6, 5, 7, 8, 4, 8, 6, 6, 7, 8, 6, 7, 7, 8, 6, 7, 8, 7, 8, 8, 8, 6, 9, 7, 8, 8, 9, 8, 7, 8, 9, 8, 9, 8, 9, 10, 8, 9, 9, 8, 10, 9, 9, 10, 8, 10, 9, 10, 9, 9

Offset

1,2

Comments

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

This sequence is unbounded.

Links

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

Rémy Sigrist, PARI program for A338283

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A336346 and A338292 for similar sequences.

Cf. A338285 (corresponding sums).

Sequence in context: A182744 A308355 A336346 * A104324 A193212 A131818

Adjacent sequences: A338280 A338281 A338282 * A338284 A338285 A338286

Keyword

nonn

Author

Rémy Sigrist, Oct 20 2020

Status

approved