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A352809
Lexicographically earliest sequence of distinct nonnegative integers such that for any proper divisor d of n the binary expansions of a(d) and a(n) have no common 1's.
3
0, 1, 2, 4, 3, 8, 5, 10, 9, 12, 6, 16, 7, 18, 20, 32, 11, 36, 13, 48, 24, 40, 14, 64, 28, 56, 52, 72, 15, 96, 17, 80, 25, 68, 88, 128, 19, 34, 104, 192, 21, 160, 22, 144, 224, 112, 23, 256, 26, 288, 84, 320, 27, 384, 120, 416, 176, 208, 29, 512, 30, 38, 352
OFFSET
1,3
COMMENTS
This sequence is a bijection from the positive integers onto the nonnegative integers (with inverse A353266); as a(1) = 0, for any prime number p, a(p) is the least value not yet in the sequence, and eventually every nonnegative integer will appear in the sequence.
EXAMPLE
The first terms, alongside their binary expansion, proper divisors and implied forbidden bits, are:
n a(n) bin(a(n)) proper divisors bin(forbidden)
-- ---- ------ --------------- --------------
1 0 0 {} 0
2 1 1 {1} 0
3 2 10 {1} 0
4 4 100 {1, 2} 1
5 3 11 {1} 0
6 8 1000 {1, 2, 3} 11
7 5 101 {1} 0
8 10 1010 {1, 2, 3} 101
9 9 1001 {1, 2} 10
10 12 1100 {1, 2, 3} 11
11 6 110 {1} 0
12 16 10000 {1, 2, 3, 4, 5} 1111
13 7 111 {1} 0
14 18 10010 {1, 2, 3} 101
PROG
(PARI) See Links section.
CROSSREFS
Cf. A027751, A353266 (inverse).
Sequence in context: A053211 A131390 A131395 * A109812 A137622 A376906
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 04 2022
STATUS
approved