cp's OEIS Frontend

A351691 Lexicographically earliest infinite sequence of distinct positive numbers such that, for n>2, a(n) has a common factor with a(n-1), shares a 1-bit in its binary expansion with a(n-1), has no common factor with a(n-2), and does not share a 1-bit in its binary expansion with a(n-2).

%I A351691 #26 Jun 25 2022 22:53:25
%S A351691 1,2,6,21,161,736,66,15,145,464,68,527,155,80,96,33,143,26,48,165,65,
%T A351691 338,14,133,209,88,10,35,273,24,40,295,531,144,136,1037,305,50,74,333,
%U A351691 129,688,20,325,299,138,132,341,1147,1184,384,261,551,608,72,141,517,770,18,57,589,1798,34,8313
%N A351691 Lexicographically earliest infinite sequence of distinct positive numbers such that, for n>2, a(n) has a common factor with a(n-1), shares a 1-bit in its binary expansion with a(n-1), has no common factor with a(n-2), and does not share a 1-bit in its binary expansion with a(n-2).
%C A351691 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).
%e A351691 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.
%Y A351691 Cf. A336957, A353989, A354087, A064413, A352763.
%K A351691 nonn
%O A351691 1,2
%A A351691 _Scott R. Shannon_, May 26 2022