OFFSET
1,2
COMMENTS
The sequence is similar to A336957 but with the addition restrictions that each new term a(n) must share a 1-bit in its binary expansion with a(n-1), while sharing no 1-bits with the binary expansion of a(n-2). To ensure the sequence is infinite each a(n) must not only have a prime factor not in a(n-1), implying no prime or prime powers can occur (see A336957), it must also have a 1-bit in its binary expansion that is a 0-bit in the binary expansion of a(n-1).
EXAMPLE
a(5) = 161 = 10100001_2 as a(4) = 21 = 10101_2, a(3) = 6 = 110_2, and 161 is the smallest unused number that shares a factor with 21, has a 1-bit in common with 21 in their binary expansions, does not share a factor with 6, has no 1-bit in common with 6 in their binary expansions, has a prime factor not in 21, and has a 1-bit in its binary expansion that is a 0-bit in the binary expansion of 21.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, May 26 2022
STATUS
approved