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.
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
Examples
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
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, PARI program
- Index entries for sequences that are permutations of the natural numbers
Programs
-
PARI
See Links section.
Comments