login
A316385
Lexicographically earliest sequence of distinct positive terms such that for any n > 0, a(n) AND a(2*n) = a(n) (where AND denotes the binary AND operator).
2
1, 3, 2, 7, 4, 6, 5, 15, 8, 12, 9, 14, 10, 13, 11, 31, 16, 24, 17, 28, 18, 25, 19, 30, 20, 26, 21, 29, 22, 27, 23, 63, 32, 48, 33, 56, 34, 49, 35, 60, 36, 50, 37, 57, 38, 51, 39, 62, 40, 52, 41, 58, 42, 53, 43, 61, 44, 54, 45, 59, 46, 55, 47, 127, 64, 96, 65
OFFSET
1,2
COMMENTS
This sequence is a permutation of the natural numbers (as odd-indexed terms are not constrained); see A316472 for the inverse sequence.
In the binary plot of the sequence, if the pixel (x, y) is on, then the pixel (2*x, y) is on.
FORMULA
Empirically:
- a(2*k) = A004755(a(k)) for any k > 0,
- a(2*k - 1) = A004761(k + 1) for any k > 0,
- a(n) = n iff n belongs to A020989.
EXAMPLE
The first terms, alongside the binary representations of a(n) and of a(2*n), are:
n a(n) bin(a(n)) bin(a(2n))
-- ---- --------- ----------
1 1 1 11
2 3 11 111
3 2 10 110
4 7 111 1111
5 4 100 1100
6 6 110 1110
7 5 101 1101
8 15 1111 11111
9 8 1000 11000
10 12 1100 11100
PROG
(PARI) See Links section.
CROSSREFS
Cf. A004755, A004761, A020989, A316472 (inverse).
Sequence in context: A255555 A191664 A118319 * A341911 A341916 A360960
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jul 01 2018
STATUS
approved