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A358919
a(0) = 0, and for any n >= 0, a(n+1) is the sum of the lengths of the runs of consecutive terms a(i), ..., a(j) with 0 <= i <= j <= n such that a(i) XOR ... XOR a(j) = a(n) (where XOR denotes the bitwise XOR operator).
3
0, 1, 3, 1, 4, 1, 5, 5, 10, 4, 12, 18, 1, 13, 8, 22, 44, 7, 52, 1, 19, 35, 10, 43, 53, 7, 68, 1, 31, 24, 56, 73, 8, 126, 105, 35, 71, 36, 71, 60, 70, 1, 124, 180, 10, 172, 41, 182, 40, 288, 1, 232, 15, 201, 4, 271, 6, 213, 1, 233, 14, 230, 25, 216, 9, 157, 115
OFFSET
0,3
COMMENTS
The 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), are:
n a(n) (i,j)'s
-- ---- ---------------------------------
0 0 N/A
1 1 (0,0)
2 3 (0,1), (1,1)
3 1 (2,2)
4 4 (0,1), (1,1), (3,3)
5 1 (4,4)
6 5 (0,1), (1,1), (3,3), (5,5)
7 5 (3,4), (4,5), (6,6)
8 10 (3,4), (4,5), (4,7), (6,6), (7,7)
9 4 (6,8), (8,8)
10 12 (3,5), (3,7), (4,4), (5,6), (9,9)
11 18 (0,8), (1,8), (10,10)
12 1 (11,11)
PROG
(C) See Links section.
CROSSREFS
Sequence in context: A242746 A363258 A327642 * A354617 A324242 A216543
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Dec 06 2022
STATUS
approved