cp's OEIS Frontend

A354420 Lexicographically earliest infinite sequence of distinct positive numbers such that, for n>3, a(n) has a common factor with a(n-2), shares a 1-bit in its binary expansion with a(n-2), has no common factor with a(n-1), and does not share a 1-bit in its binary expansion with a(n-1).

%I A354420 #6 Jun 26 2022 00:12:25
%S A354420 1,2,5,18,65,6,25,4,35,12,49,8,7,24,133,10,21,34,9,22,105,16,3,20,33,
%T A354420 14,81,38,129,26,69,40,23,32,207,304,15,112,135,56,195,28,99,136,39,
%U A354420 88,261,50,141,80,47,64,423,584,51,76,17,36,323,44,19,68,57,70,153,98,285,194,45,82,165
%N A354420 Lexicographically earliest infinite sequence of distinct positive numbers such that, for n>3, a(n) has a common factor with a(n-2), shares a 1-bit in its binary expansion with a(n-2), has no common factor with a(n-1), and does not share a 1-bit in its binary expansion with a(n-1).
%C A354420 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.
%e A354420 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.
%Y A354420 Cf. A098550, A351691, A064413, A353990, A336957, A353989, A354087, A352763.
%K A354420 nonn
%O A354420 1,2
%A A354420 _Scott R. Shannon_, May 26 2022