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A346516
A variant of Van Eck's sequence: For n >= 0, a(n+1) is the result of combining by XOR the numbers k such that k < n and a(k) = a(n). Start with a(0)=0.
2
0, 0, 0, 1, 0, 3, 0, 7, 0, 1, 3, 5, 0, 9, 0, 5, 11, 0, 11, 16, 0, 26, 0, 14, 0, 24, 0, 0, 26, 21, 0, 1, 10, 0, 31, 0, 62, 0, 29, 0, 56, 0, 31, 34, 0, 54, 0, 26, 9, 13, 0, 52, 0, 6, 0, 50, 0, 4, 0, 60, 0, 6, 53, 0, 58, 0, 5, 4, 57, 0, 68, 0, 1, 21, 29, 38, 0
OFFSET
0,6
COMMENTS
XOR denotes the bitwise XOR operator.
This sequence is unbounded, and contains infinitely many 0's.
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k's
-- ---- --------------------
0 0 None
1 0 0
2 0 0, 1
3 1 None
4 0 0, 1, 2
5 3 None
6 0 0, 1, 2, 4
7 7 None
8 0 0, 1, 2, 4, 6
9 1 3
10 3 5
11 5 None
12 0 0, 1, 2, 4, 6, 8
13 9 None
14 0 0, 1, 2, 4, 6, 8, 12
15 5 11
PROG
(PARI) { p=vector(123); v=0; for (n=0, 76, print1(v", "); w=p[1+v]; p[1+v]=bitxor(p[1+v], n); v=w) }
CROSSREFS
Sequence in context: A137436 A099893 A135534 * A337767 A249904 A324875
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Sep 27 2021
STATUS
approved