OFFSET
1,2
COMMENTS
A144795 gives the numbers without isolated 1's in base-2 representation.
This sequence is conjectured to be a permutation of the natural numbers.
This sequence has similarities with A269361: here we require that the product of two consecutive terms has no isolated 1, there the product of two consecutive terms has only isolated 1's, in base-2 representation.
For any k > 0:
- a(2*k-1) belongs to A091072,
- a(2*k) belongs to A091067.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A289194
EXAMPLE
The first terms, alongside a(n)*a(n+1) in binary, are:
n a(n) a(n)*a(n+1) in binary
-- ---- ---------------------
1 1 11
2 3 110
3 2 1100
4 6 11000
5 4 11100
6 7 111000
7 8 1100000
8 12 111100
9 5 110111
10 11 1100011
11 9 1111110
12 14 11100000
13 16 11110000
14 15 11000011
15 13 11110111
16 19 110001111
17 21 111001110
18 22 11011100
19 10 11100110
20 23 110000111
MATHEMATICA
a = {1}; Do[k = 1; While[Nand[! MemberQ[a, k], ! MemberQ[Length /@ DeleteCases[Split[IntegerDigits[k Last[a], 2]], s_ /; First@ s == 0], 1]], k++]; AppendTo[a, k], {n, 2, 67}]; a (* Michael De Vlieger, Jun 29 2017 *)
CROSSREFS
KEYWORD
AUTHOR
Rémy Sigrist, Jun 28 2017
STATUS
approved