cp's OEIS Frontend

A229072 Lexicographically earliest sequence of distinct natural numbers such that, for any number n in the sequence, the positions of the 1's in the binary representation of n are in the sequence, whereas the positions of the 0's are not.

%I A229072 #13 Apr 05 2020 22:25:43
%S A229072 1,4,9,18,36,72,144,289,578,1156,2312,4624,9248,18496,36992,73984,
%T A229072 147969,295938,591876,1183752,2367504,4735008,9470016,18940032,
%U A229072 37880064,75760128,151520256,303040512,606081024,1212162048,2424324096,4848648192,9697296384
%N A229072 Lexicographically earliest sequence of distinct natural numbers such that, for any number n in the sequence, the positions of the 1's in the binary representation of n are in the sequence, whereas the positions of the 0's are not.
%C A229072 The position 1 corresponds to the most significant bit.
%H A229072 Paul Tek, <a href="/A229072/b229072.txt">Table of n, a(n) for n = 1..3321</a>
%H A229072 Paul Tek, <a href="/A229072/a229072_1.txt">PARI program for this sequence</a>
%F A229072 a(n) = Sum_{a(i) <= n+1} 2^(n+1-a(i)), for any n>1, with a(1)=1.
%e A229072 1 has a 1 at position 1, and no 0's, hence 1 belongs to the sequence.
%e A229072 2 has a 0 at position 2, hence 2 cannot belong to the sequence.
%e A229072 3 has a 1 at position 2, as 2 cannot belong to the sequence, 3 cannot either.
%e A229072 4 has a 1 at position 1, and 0's at positions 2 and 3, hence 4 belongs to the sequence.
%e A229072 9 has 1's at positions 1 and 4, and 0's at positions 2 and 3, hence 9 belongs to the sequence.
%o A229072 (PARI) See Link section.
%Y A229072 Cf. A098645.
%K A229072 nonn,base
%O A229072 1,2
%A A229072 _Paul Tek_, Sep 12 2013