OFFSET

1,3

COMMENTS

This sequence is unbounded (if the sequence was bounded, say by m, then, by the pigeonhole principle, some value v <= m would appear infinitely many times, and for any k > 0, the k-th occurrence of v would be followed by a value >= k, a contradiction).

LINKS

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

Rémy Sigrist, C++ program

Rémy Sigrist, PARI program

EXAMPLE

The first terms, alongside an appropriate set of points, are:

n a(n) Points

-- ---- -----------------------------------

1 1 N/A

2 1 (1,1)

3 2 (1,1), (2,1)

4 2 (1,1), (3,2)

5 2 (1,1), (4,2)

6 3 (3,2), (4,2), (5,2)

7 3 (2,1), (4,2), (6,3)

8 3 (1,1), (4,2), (7,3)

9 3 (2,1), (5,2), (8,3)

10 4 (6,3), (7,3), (8,3), (9,3)

11 4 (1,1), (4,2), (7,3), (10,4)

12 4 (2,1), (5,2), (8,3), (11,4)

13 3 (4,2), (8,3), (12,4)

14 5 (6,3), (7,3), (8,3), (9,3), (13,3)

15 5 (2,1), (5,2), (8,3), (11,4), (14,5)

PROG

(C++) // See Links section.

(PARI) \\ See Links section.

CROSSREFS

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Aug 14 2024

STATUS

approved