OFFSET
1,2
COMMENTS
The sequence is similar to A098550 but with the addition restrictions that each new term a(n) must share a 1-bit in its binary expansion with a(n-2), while sharing no 1-bits with the binary expansion of a(n-1). Unlike A351691 no additional restrictions on the factors or 1-bits of a(n) are required for the sequence to be infinite. The sequence is conjectured to be a permutation of the positive integers.
EXAMPLE
a(5) = 65 = 1000001_2 as a(4) = 18 = 10010_2, a(3) = 5 = 101_2, and 65 is the smallest unused number that shares a factor with 5, has a 1-bit in common with 5 in their binary expansions, does not share a factor with 18, has no 1-bit in common with 18 in their binary expansions.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, May 26 2022
STATUS
approved