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A355413 Lexicographically earliest infinite sequence of positive numbers such that, for n>1, a(n) AND a(n-1) is distinct from all previous AND operations between adjacent terms, where AND is the binary AND operator.

%I A355413 #13 Jul 01 2022 09:38:25
%S A355413 0,1,3,3,6,5,7,7,14,9,11,11,14,13,15,15,30,17,19,19,22,21,23,23,30,25,
%T A355413 27,27,30,29,31,31,62,33,35,35,38,37,39,39,46,41,43,43,46,45,47,47,62,
%U A355413 49,51,51,54,53,55,55,62,57,59,59,62,61,63,63,126,65,67,67,70,69,71,71,78,73,75,75
%N A355413 Lexicographically earliest infinite sequence of positive numbers such that, for n>1, a(n) AND a(n-1) is distinct from all previous AND operations between adjacent terms, where AND is the binary AND operator.
%C A355413 Each term must be chosen so that a subsequent term can always been found. This implies, for example, no power of 2 can ever be a term as the result of an AND operation between such a number and any following number will be either 0 or the power of 2, both of which have already appeared as the result of AND operations.
%C A355413 Every a(n) where n is odd is a fixed point.
%H A355413 Scott R. Shannon, <a href="/A355413/a355413.png">Line graph of the first 100000 terms</a>.
%e A355413 a(3) = 3 as a(2) = 3 and 3 AND 3 = 3, which has not occurred earlier for any AND's between adjacent terms. Note that a(3) cannot equal 2 = 10_2 as the result of any subsequent AND operation with 2 would be 0 or 2, both of which have already occurred.
%Y A355413 Cf. A007088, A129760, A338824.
%K A355413 nonn,base
%O A355413 0,3
%A A355413 _Scott R. Shannon_, Jul 01 2022