A336346 Lexicographically earliest sequence of positive integers such that for any distinct m and n, Product_{k = m+1-a(m)..m} a(k) <> Product_{k = n+1-a(n)..n} a(k).

1, 2, 2, 3, 2, 3, 4, 2, 3, 4, 3, 4, 4, 3, 5, 2, 3, 4, 5, 3, 3, 3, 4, 5, 4, 4, 5, 5, 3, 4, 5, 6, 3, 3, 4, 5, 5, 4, 6, 4, 4, 5, 5, 6, 5, 5, 6, 5, 6, 7, 2, 3, 4, 5, 6, 5, 6, 6, 5, 6, 7, 3, 3, 4, 5, 6, 6, 5, 7, 3, 4, 4, 5, 5, 7, 4, 3, 5, 6, 4, 6, 4, 5, 6, 7, 5, 5

Offset

1,2

Comments

In other words, for any n > 0, the product 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 A336346

Example

The first terms, alongside the corresponding products, are:
  n   a(n)  a(n+1-a(n))*...*a(n)
  --  ----  --------------------
   1     1                     1
   2     2                     2
   3     2                     4
   4     3                    12
   5     2                     6
   6     3                    18
   7     4                    72
   8     2                     8
   9     3                    24
  10     4                    96

Prog

(PARI) See Links section.

Crossrefs

See A338283 for a similar sequence.

Cf. A338118 (corresponding products).

Sequence in context: A238458 A182744 A308355 * A338283 A104324 A193212

Adjacent sequences: A336343 A336344 A336345 * A336347 A336348 A336349

Keyword

nonn

Author

Rémy Sigrist, Oct 21 2020

Status

approved