A336346 - OEIS

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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

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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