A352812 - OEIS

A352812

Lexicographically earliest sequence of distinct nonnegative integers such that for any n and k coprime the binary expansions of a(n) and a(k) have no common 1's.

%I #13 Apr 09 2022 17:38:15

%S 0,1,2,4,8,3,16,5,32,9,64,6,128,17,10,256,512,7,1024,12,18,65,2048,33,

%T 4096,129,34,20,8192,11,16384,257,66,260,24,35,32768,261,130,13,65536,

%U 19,131072,68,40,2049,262144,36,524288,264,514,132,1048576,37,72,21

%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n and k coprime the binary expansions of a(n) and a(k) have no common 1's.

%C The n-th row of A038566 gives the k's to consider when computing a(n).

%H Rémy Sigrist, <a href="/A352812/b352812.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A352812/a352812.png">Colored logarithmic scatterplot of the first 10000 terms</a> (where the color is function of A052126(n))

%H Rémy Sigrist, <a href="/A352812/a352812.gp.txt">PARI program</a>

%e The first terms, alongside their binary expansion, the corresponding k's and the implied forbidden bits, are:

%e n a(n) bin(a(n)) k's bin(forbidden)

%e -- ---- --------- ------------------------------- --------------

%e 1 0 0 {1} 0

%e 2 1 1 {1} 0

%e 3 2 10 {1, 2} 1

%e 4 4 100 {1, 3} 10

%e 5 8 1000 {1, 2, 3, 4} 111

%e 6 3 11 {1, 5} 1000

%e 7 16 10000 {1, 2, 3, 4, 5, 6} 1111

%e 8 5 101 {1, 3, 5, 7} 11010

%e 9 32 100000 {1, 2, 4, 5, 7, 8} 11101

%e 10 9 1001 {1, 3, 7, 9} 110010

%e 11 64 1000000 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 111111

%e 12 6 110 {1, 5, 7, 11} 1011000

%o (PARI) See Links section.

%Y Cf. A038566, A052126, A352809.

%K nonn,base

%O 1,3

%A _Rémy Sigrist_, Apr 04 2022