

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
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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



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



STATUS

approved



