OFFSET
0,3
COMMENTS
This sequence is a variant of A331614 and A332518; here we use binary XOR, there addition and multiplication, respectively.
This sequence is unbounded (if the sequence was bounded, with greatest value m, then, by the pigeonhole principle, some value, say v, would appear infinitely many times, and the next value after the (m+1)-th occurrence of v would be > m, a contradiction).
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, C program
Rémy Sigrist, Scatterplot of the first 250000 terms
EXAMPLE
The first terms, alongside the corresponding pairs (i,j)'s, are:
n a(n) (i,j)'s
-- ---- ---------------------------------------------------------
0 0 N/A
1 1 (0,0)
2 2 (0,1), (1,1)
3 1 (2,2)
4 3 (0,1), (1,1), (3,3)
5 4 (0,2), (1,2), (2,3), (4,4)
6 2 (2,5), (5,5)
7 5 (0,3), (1,3), (2,2), (3,4), (6,6)
8 4 (0,5), (1,5), (4,6), (7,7)
9 5 (2,5), (3,6), (4,8), (5,5), (8,8)
10 6 (0,5), (1,5), (3,8), (4,6), (7,7), (9,9)
11 8 (0,8), (1,8), (2,6), (3,5), (3,10), (5,6), (6,9), (10,10)
12 2 (6,11), (11,11)
PROG
(C) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Dec 06 2022
STATUS
approved