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A358799 a(0) = 0, and for any n >= 0, a(n+1) is the number of ways to write a(n) = a(i) XOR ... XOR a(j) with 0 <= i <= j <= n (where XOR denotes the bitwise XOR operator). 3
0, 1, 2, 1, 3, 4, 2, 5, 4, 5, 6, 8, 2, 11, 2, 13, 6, 14, 10, 9, 9, 12, 14, 16, 2, 24, 6, 29, 5, 23, 3, 27, 12, 23, 9, 26, 17, 13, 26, 19, 15, 32, 4, 46, 2, 51, 1, 45, 6, 48, 6, 49, 7, 41, 9, 47, 10, 49, 17, 37, 21, 38, 23, 36, 24, 49, 30, 48, 24, 52, 22, 45 (list; graph; refs; listen; history; text; internal format)
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, C program
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
Sequence in context: A358103 A112382 A117384 * A125160 A359027 A366691
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Dec 06 2022
STATUS
approved

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Last modified March 1 13:16 EST 2024. Contains 370433 sequences. (Running on oeis4.)