OFFSET
1,6
COMMENTS
This sequence is unbounded: by contradiction:
- if the sequence was bounded, say a(n) <= M for any n > 0, then some value, say v, would appear infinitely many times, say at indices (b(1), b(2), ...),
- hence for any k > 0, a(b(k)+1) >= (k-1)*(k-2)/2,
- and for k > 2 + sqrt(2*M), a(b(n)+1) > M , a contradiction, QED.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A308639
EXAMPLE
The first terms, alongside the pairs (i,j) such that 0 < i < j < n-1 and the points (i, a(i)), (j, a(j)) and (n-1, a(n-1)) are aligned, are:
n a(n) (i,j)'s
-- ---- -----------------------------------
1 0 none
2 0 none
3 0 none
4 1 (1,2)
5 0 none
6 3 (1,2), (1,3), (2,3)
7 1 (3,4)
8 0 none
9 6 (1,2), (1,3), (1,5), (2,3), (2,5), (3,5)
10 3 (3,4), (3,6), (4,6)
11 1 (1,4)
12 1 (4,7)
13 3 (4,7), (4,11), (7,11)
14 1 (6,10)
PROG
(C) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 13 2019
STATUS
approved